It’s definition is: Basically, when the sweets get shared out, floor divide tells you how many sweets each child gets. Condition: You are not allowed to use modulo or % operator.. If one adopts a convention that integer division (by a positive number) truncates toward negative infinity then one would get a different conventional remainder. The modulo operation is supported for integers and floating point numbers. Description. Click me to see the solution. 3. Just like in multiplication, when one but not both numbers are negative, the answer If both numbers are negative, the answer will be positive. (common) Modulus is the desired behavior, and dealing with negative remainders is a pain. Found inside – Page 150Of positive numbers the larger is also the greater , but of negative numbers the ... or equal numbers be subtracted from them , then is the first remainder ... When the first operand is a negative value, the return value will always be negative, and vice versa for positive values. Therefore, -97 mod 11 equals 2! Subscribe to this Thread… Hello, I'm looking for a way in C to get the remainder of a negative number such that the remainder is positive, i.e. using truncation toward negative infinity rather than truncation toward zero. I'd like to avoid using a floating point function (floor ()); integer math only. . Here “a” is dividend and “b” is the divisor. How to Find Number of Factors? Not bad. Anyone can write the equation and use the negative number as a remainder, but according to Euclid’s division algorithm lemma, it can never be negative. The best method to find the remainder of this problem is the remainder theorem. This concept should apply here as well. If the result is an integer, say q, then we have. In other words, applying the remainder theorem we must get P\left( c \right) = 0. The remainder is a negative number:-3. Often you need to know the oddness and evenness of an integer. To do that, we will need to substitute the value of “c” into the polynomial P\left( x \right), and simplify. *fix (a./b) . In number theory, remainders are always positive. The modulus operator can also work with negative operands. Anyone can predict the output of a modulus operator when the both operands are positive. Remainder of 21.5%5 = 1.5 Remainder of 100%5.5 = 1.0 Remainder of = 1.1999999999999993 Remainder of 43%17 = 1.0. To answer this question, remember that when a number is divided by another and the remainder is zero, that means the number dividing the other is a factor of that number. Then, go down by multiplying that partial quotient you put up with the terms of the divisor. Click Here to read Positive Remainder Theorem. Evaluating c = + 1 into the given polynomial…, By getting an answer of zero, this shows that x - 1 is indeed a factor of. The remainder operator can be used with negative integers. If you need a refresher on how to divide polynomials using the Long Method, check out my separate tutorial: Polynomial Long Division. Hello, I'm looking for a way in C to get the remainder of a negative number such that the remainder is positive, i.e. Found inside – Page 21For any integer I and any natural number n there is a unique pair of numbers a and b such that ... This is because the remainder is always non negative . Write a C program to allocate a block of memory for an array. 10. The MOD function returns the remainder after division. So -23 rem 5 = -3. About Modulo Calculator . Enter the divisor. Returns the remainder when Dividend is divided by Divisor. To find the remainder of a polynomial divided by some linear factor, we usually use the method of Polynomial Long Division or Synthetic Division. Write a C program to return the quotient and remainder of a division. Returns the least common multiple (a non-negative number) of the n s; non-integer n s, the result is the absolute value of the product divided by the gcd.If no arguments are provided, the result is 1.If any argument is zero, the result is zero; furthermore, if any argument is exact 0, the result is exact 0. (and many other computer languages) use round-towards-zero for. When we divide one integer, b, by some other integer, a ≠ 0, the result is either an integer or its not. The value of the remainder can never be negative in any case. Floor division is also used to carry out Euclidean division, but unlike the modulo operator, floor division yields the quotient, not the remainder. number1 Required. We can find the number of factors of a given number using the following steps. -11 divided by 5 equals -2 remainder 1. Which gives positive remainder of 64 to be 9 and its Negative remainder to be -2. Multiply the variable reverse by 10 and add the remainder into it. It is used to find the remainder. If both a and N are positive, in all the programming languages, a mod N is the remainder of the Euclidean division. Objec­tive: Write Given two integers ‘number’ and ‘divisor’, Write an algorithm to find the remainder if ‘number’ is divided by ‘divisor’.. The Python integer division operator, //, is called floor divide. Found inside – Page 31The justification of this process of determining the sign of the partial remainder is as follows : A negative binary number may be indicated by the ... Where A2 is the leftmost cell with data. What happens whe… i.e. However, C#. Similarly, 64 can be written as 11 x 5 + 9 or 64 = 11 x 6 – 2. Negative factors are just factors with negative sign. x % y always returns results with the sign of x.. Running the above program: Enter an integer: -6 Enter another integer: 4 The remainder is: -2 -6 is not evenly divisible by 4 A remainder can be negative. Like in Your example -11/6 will give -5 as the remainder and the quotient will be -1. See it this way -11 = 6 x (-1) + (-5). Hope this helps! The remainder of 8, 10 and 12 imply that the negative remainders are -5, -3 and -1 respectively. But is that really the case? But when it comes to the negative numbers, different languages give different outputs. "7 divided by 2 equals 3 with a remainder of 1" Each part of the division has names: Which can be rewritten as a sum like this: Polynomials. The parrot gets any leftover coins. $$\frac{{62 \times 63 \times 64}}{{66}}$$   ==R==> $$\left( { - 4} \right) \times \left( { - 3} \right) \times \left( { - 2} \right)$$    ==R==> -24. Factors of 8 are 1, 2, 4, and 8. Calculating factors of 206457. However, a true modulus operator would always return a positive value, so 21 modulo 5 would equal 4. The factors of 18 are 1, 2, 3, 6, 9, 18. Again, the remainder values from two different methods are equal! It's 24 in our case. Here, we have used both the theorem same time as our convenient. Highlight cells with even numbers: =MOD (A2,2)=0. The polynomial remainder theorem says that for a polynomial p (x) and a number a, the remainder on division by (x-a) is p (a). Code: x = 5 y = 2 r = x % y print (‘Remainder is:’, r) Output: Explanation:In the above example x = 5 , y =2 so 5 % 2 , 2 goes into 5 two times which yields 4 so The value of “c” is obtained when the linear factor is expressed in the form x - c. Since the divisor is x + 2, we have x - \left( { - 2} \right) therefore c = - \,2. First of all you need to understand what are positive remainder and negative remainder? As you can see, the remainder that came out using remainder theorem is equal to the remainder found by synthetic division. For example, -21 % 5 === -1, because the remainder always takes the sign of the left number. we can say that the remainder when 15 is divided by 4 is -1. -11 divided by 5 equals -2 remainder 1. This is a common programming trick. Also, 96 can be written as 11 x 8 + 8 or 96 = 11 x 9 – 3. What is the remainder when 100 is divided by 11? But according to the formula y=xq + r (q = quotient, r = remainder): -11 = 5q + r. If q = -2 and r = 1 as you said, then: -11 = 5 (-2) + (1) -11 = -10 + 1. Remainders and Divisibility. Posted by lenduha on December 28, 2011. Found inside – Page 13However, in C++ and other languages, the remainder of a negative number is either zero or negative. An easy way to make sure there are no negative ... r = rem (a,b) returns the remainder after division of a by b , where a is the dividend and b is the divisor. a modulo 0 is undefined in most systems, although some do define it as a. Value := Mod (Dividend, Divisor) The sign of the result is always the same as the sign of the first parameter. Found inside – Page 135( As it is impossible to check directly all negative numbers , we have to find a ... Because we want to evaluate the remainder of the division between P ( x ) ... Find the remainder after division by a negative divisor for a set of integers including both positive and negative values. Let's take the example from the one of previous paragraphs, so enter 250. For example, “5 mod 3 = 2” which means 2 is the remainder when you divide 5 by 3. Be especially careful when corralling random numbers into a smaller range with the modulus operator, e.g. The pattern is rather simple. We already know from earlier lessons that n, d, quotient, and remainder must be integers such that remainder ? Found inside – Page 126Return the new digits and the last remainder as the converted number. There are two not-so-obvious ... The first involves dealing with negative numbers. I don't think there isn't any need to check if the number is negative. A simple function to find the positive modulo would be this - Edit: Assumin... This operator returns the remainder left over when one operand is divided by a second operand. • The previous algorithm also works for signed numbers (negative numbers in 2’s complement form) • We can also convert negative numbers to positive, multiply the magnitudes, and convert to negative if signs disagree • The product of two 32-bit numbers can be a 64-bit number--hence, in MIPS, the product is saved in two 32-bit registers 0 and d?0. … It always takes the sign of the dividend. Standard Pascal and ALGOL 68, for example, give a positive remainder (or 0) even for negative divisors, and some programming languages, such as C90, leave it to the implementation when either of n or a is negative (see the table under § In programming languages for details). Bring down the first coefficient below the horizontal line. Found inside – Page 351If the remainder is negative , then the instruction of this line skips to ... of the high order bits of the negative number and deposit it in line 154 . The long division of this problem is shown below. a/b = q with remainder r; Such that: b*q + r = a and 0 <= r < b; Now, if we want this relationship to extend to negative numbers, there are a couple of ways of handling this corner case. Found inside – Page 112A remainder between 32767 and 65536 would be printed as a negative number because of the way negative numbers are stored . Systems with different integer ... Remainder with Negative Integers, General Discussion. Notice, 35 and 42 is divisible by 7. The rule is: From the two pieces (the quotient and the remainder) the original integer can be put back together: You may wish to practice with the following: Five pirates find a chest of 123 gold coins and Basically, the remainder will be as close to 0 as possible, and in the case where positive and negative To make it easier, create a table with two columns and write the number above it. The Ada "mod" operator uses this convention. Found inside – Page A-6A certain number when divided by 899 leaves the remainder 63. ... For example: (+5) + (+2) = +7 (b) Sum of two negative numbers is a negative number. For example, 8 % -3 = 8 – ( -3 * trunc(8/-3) ) = 8 – ( -3 * trunc(-2.666..) (occasional) Negative numbers have to be handled specially anyway, so the behavior doesn't matter. Floor division and modulo are linked by the following identity, x = (x // y) * y + (x % y) , which is why modulo also yields unexpected results for negative numbers, not just floor division. The output is the remainder when a is divided by b. Conversion from negative remainder to the corresponding positive remainder and vice versa. We already know from earlier lessons that n, d, quotient, and remainder must be integers such that remainder ? The large value of exponent in {7{x^{12}}} doesn’t bother me because there will be a lot of zeroes since there are many missing x-terms! In Mathematics, where these conventions stem from, there is no assertion that modulo arithmetic should yield a positive result. Eg. 1 mod 5 = 1, b... It is nice to see the connection! Found inside – Page 322By exclusively accepting non-negative values of the remainder, the number of such comparators can be more that halved (a instead of 2a + 1), changing the ... The modulo operation (abbreviated “mod”, or “%” in many programming languages) is the remainder when dividing. Place the product below. Found inside – Page 43-3(The And given we have number always [0.111111] z n = 1. is calculated as ... Note that the remainder for the restoring method is always negative, ... Found inside – Page 26This remainder , if it were positive , might , as in other cases of division , be prefixed to the next figure . But the remainder is negative , while the ... Found inside – Page 54Read al-Samaw'al's rules for operating with positive and negative numbers. ... “If we subtract a negative number from a positive number, the remainder is ... result Required. (occasional) Negative numbers have to be handled specially anyway, so the behavior doesn't matter. Multiply that by the number in the “box”. We get a positive remainder when a a is negative by repeated addition of b. b. Found inside – Page 21a negative number and hence it is called a negative remainder. For example, when 491 is divided by 17, the remainder (#) = 15 or 15 – 17 = 15 or –2(negative ... The value of { - 1}, when raised to some power, will simply alternate either to positive 1 or negative 1. Both arguments are required. But a remainder never be negative, then remainder is given by (66 - 24) = 42. $$\frac{{14 \times 15}}{8}$$  ==R==> $$\frac{{6 \times 7}}{8}$$  ==R==> 2 [by positive remainder theorem] This depends on your convenience. Add the column of constants and place the sum below the horizontal line. Floor division always rounds away from zero for negative numbers, so -3.5 will round to -4, but towards zero for positive numbers, so 3.5 will round to 3. Divide the first term of the dividend by the first term of the divisor. Next, take a look at the divisor. Found inside – Page 403... any remainder , write down the quotient of such division with a negative ... not divisible by the divisor without remainder , add such a negative number ... In this tutorial, you have learned how to use the PostgreSQL MOD() function to find the remainder after division of one number by another. The problem here is that in Python the % operator returns the modulusand in Java it returns the remainder. -11 % 5 == -1 11 % -5 == 1 -11 % -5 == -1. The remainder operator can be used with negative integers. In this case, 2 x 1892 = 3784. In C language, modulus is calculated as, a % n = a – ( n * trunc( a/n ) ). This might not be very clear right now, but you will understand this much better after watching these examples. For the above example this means 5 mod 3 = 2 following the definition is 5 - floor(5/3)*3 = 2. Remainder (modulus) operator for negative values in C & C++. Found inside – Page 26This remainder , if it were positive , might , as in other cases of division , be prefixed to the next figure . But the remainder is negative , while the ... Modulo. Testing the integer values 1 through 4 for division into 18 with a 0 remainder we get these factor pairs: (1 and 18), (2 and 9), (3 and 6). So x squared minus five X plus seven is divided by X plus one. To highlight cells containing odd or even numbers, use the following Excel Mod formula that divides the number by 2, and then checks for a remainder of 1 and 0, respectively: Highlight cells with odd numbers: =MOD (A2,2)=1. Or: how to avoid Polynomial Long Division when finding factors. using truncation toward negative infinity rather than truncation toward zero. Example 4: Determine if x - 1 is a factor of. remainder and modulo differ on negative arguments -- the remainder always has the sign of the dividend ... if n is negative, the number is rounded (- n) digits to the left of the decimal point. Based on the C99 Specification: a == (a / b) * b + a % b We can write a function to calculate (a % b) == a - (a / b) * b ! int remainder(int a, i... Note that nonzero results are always negative if the divisor is negative. Found inside – Page 169And that if , from 5 a positive number , you have to subtract a negative number , the true remainder will be got , in like manner , by changing the sign of ... always have a non-negative integer r such that d*x+r = y. 32 can be written as 11 x 2 + 10 or 32 = 11 x 3 – 1. It is great to see that the remainder obtained using the long method division, came out to be equal with the remainder found using the Remainder Theorem Method. The negative remainder would be -5. The % operator in C is not the modulo operator but the remainder operator. Modulo and remainder operators differ with respect to negative val... Number is the number to be divided, and divisor is the number used to divide. This is the same as repeatedly adding −b. Watch the video to understand the concept of Negative Remaind... Did you know: N=7x+5 = 7y-2 (A remainder of + 5 can also be written as -2 on division with 7).. Type the initial number - dividend - into the first box. Here, the remainder will have the same sign as the divisor, so my divisor is positive that’s why the remainder is also positive vice versa. If you have a large number, it's more difficult to do the mental math to find its factors. There are three ways to reverse a number in Java: Reverse a number … The MOD function takes two arguments: number and divisor. An example of this is the24-hour digital clock, which resets itself to 0 at midnight. Example 1: Use Polynomial Long Division to find the remainder of the problem below. 1. Found inside – Page 96Division using negative numbers is permitted in PowerShell. When a positive number is divided by a negative number, the result is negative. Remainder ... Click Here for Solved Examples on Number System, Negative Remainder Theorem and its Application. Finding the Remainder using Long Division Method. Find the remainder when $$\frac{{14 \times 15}}{8}.$$, Solution: This example uses negative numbers with the modulus operator. 3. The other answers have explained in C99 or later, division of integers involving negative operands always truncate towards zero . Note that, in... In the above question, n = -17, d = 7 The goal is to find a value for the quotient such that 0 ? Found inside – Page 443When a numbers are added , the sign bit is negative remainder results , a 0 not complemented . When one appears in the quotient . When the positive number ... The purpose of this post is not explaining modular arithmetic, but if you are not familiar with it and interested in learning more, please take a look at wikipedia page as a starting point. Test Data and Expected Output : Input numerator : 2000 Input denominator : 235 quotient = 8, remainder = 120. There's some more information about it in this question. … What is the multiple of 6 that is less than –23 and closest to –23? CCSS.Math: HSA.APR.D.6. Found inside – Page 310If you want to read that out loud, say “seven remainder three.” f'\ Negative Numbers Adding Negative Numbers With whole numbers you can say, ... Whereas, n and quotient can be any integers (positive, negative, or zero). Now, let’s check if the remainder we found using long division method is indeed correct. All of the above information and methods generally apply to factoring negative numbers. If the answer comes out negative, Remainder of 21.5%5 = 1.5 Remainder of 100%5.5 = 1.0 Remainder of = 1.1999999999999993 Remainder of 43%17 = 1.0. To account for a negative input or result, we’ll use abs() to modify what is returned to be a positive number.. Finding the Quotient and Remainder in One Function. Example:. Found inside – Page 165The remainders of a negative number . ... 6 ( which we call the ordinary remainder ) +2 ( the numerical value of the negative remainder ) = the divisor 8. Returns the least common multiple (a non-negative number) of the n s; non-integer n s, the result is the absolute value of the product divided by the gcd.If no arguments are provided, the result is 1.If any argument is zero, the result is zero; furthermore, if any argument is exact 0, the result is exact 0. In number theory, remainders are always positive. i.e. However, if you compare the modulo operation with 0 , then it doesn’t matter which operand is negative. Considering a question: ... we want to find the remainder when x squared minus five X plus seven. division, which is where the negative remainder comes in. % can produce a negative result even with a positive divisor. The best method to find the remainder of this problem is the remainder theorem. It’s time to perform synthetic division to the example above. Why? For example: See, the positive remainder is 2 which are just more than 35 and -5 is just less than 42. Can a modulus be negative? % can be negative as it is the remainder operator , the remainder after division, not after Euclidean_division .... This function is often called the remainder operation, which can be expressed as r = a - b. There are basically only three cases that actually occur in practice: 1. Like in Your example -11/6 will give -5 as the remainder and the quotient will be -1. Repeat the process of multiplying the number below the horizontal with the number in the “box” and adding the columns of constants until such time you reach the last column. Perform subtraction. The value of { - 1}, when raised to some power, will simply alternate either to positive 1 or negative 1. nextInt % 3 will give you numbers -2 .. +2 not 0 .. 2 as most would expect. Say, a number 37 is divided by 7 then what would be the remainder? : Input numerator: 2000 Input denominator: 235 quotient = 8, 10 and 12 imply that the of! Program to allocate a block of memory for an array refresher on to! This function is often called the remainder occasional ) negative numbers is a pain 2 + 10 32! It as a plus seven is our remainder 'd like to avoid using a floating point function ( floor ). Term “ mod ” stands for the modulo operator gives a value that is less than 42 11 % ==... For a set of integers involving negative operands always truncate towards zero the subject came up 24! ) = 42 comes in never be negative, or zero ) 2 when divided by is... Finding factors where you will the dividend or the divisor is negative ( below horizontal!, which is also a positive remainder and the quotient to be -2 be handled specially,. I am specifically thinking of the Euclidean division always takes the sign of the problem below a non-negative r... B... a remainder of - \,2 being the modulus operator, e.g on... Uses this convention as our convenient 4, and dealing with negative integers the value... The... found inside – Page A-6A certain number when divided by 4 is.... In order for x - 1 is a negative value, so the remainder.! Convention that rem ( a,0 ) is the remainder negative sign number, the difference in the being! I am specifically thinking of the dividend random numbers into a smaller range with the of... Remainder found by synthetic division: the steps may sound “ confusing ” but wait until you an! % to denote a modulo operator is a % n = a – n. See, remainder of negative number answer will be -1 n't any need to understand are. 6 that is related to the conventions of other languages remainder which is also a floating number... Is shown below repeated addition of b. b without remainder 2 + 10 or 32 = 11 x 3 1! Into it of modulo operator but the remainder must be integers such that remainder the return value will be. 6Find the remainder that came out remainder of negative number this method for more practice as well of 1 remainder to the positive. For the modulo operation, which can be expressed as r = a b. Call the ordinary remainder ) +2 ( the numerical value of { 1. Numerical value of { - 1 to be expressed in positive value, 21! Calculator will return to you your result - the same as that of a division make sure there basically. Number to be handled specially anyway, so 21 modulo 5 would -5! The mod function takes two arguments: number and divisor the term “ mod ” something, divide. N'T think there is no assertion that modulo arithmetic should yield a positive number... found inside – Page remainders... Dividing integer numbers, both positive and therefore equal, or zero ) ( A2,2 ) =0 give numbers! Matches with the modulus the answer will be substituted in the result the initial -! Our modulo calculator will return to you your result - the remainder found using synthetic division matches with the part! Is by subtracting them after watching these Examples much better after watching these Examples -3 and -1.. Out with x squared methods are equal 1 is a pain ( 8.435 ) floor polynomials. Function takes two arguments: number and divisor is known to be equal to the higher! It ’ s time to perform the operation as if both operands are positive remainder negative. Remainders of a % b is the desired behavior, and vice versa nextint % 3 will you., 6, 9, 18 ” but wait until you see an example 0 at.... Numbers: =MOD ( A2,2 ) =0 vice versa 8 are 1, 2 the! 54Read al-Samaw'al 's rules for operating with positive and negative remainders that ’ s begin taking... Is no assertion that modulo arithmetic should yield a positive divisor by plus... Those things that i know, but you will work this out using remainder theorem must. To bring down, so the behavior does n't matter 2 you can positive. Modulo makes a well-reasoned exception to the negative remainder theorem we must get P\left ( C )! Plus one is signed and holds a Option 3: … there are no negative especially careful when random. 0.. 2 as most would expect of 2 ( very common the. Only the coefficients and constant of the divisor 7 9 ] ; =! Applying the remainder factoring negative numbers we get a positive value, the return value will always be negative it. Be -5 and -23 mod 5 = 1, because the remainder after division, not after Euclidean_division problem.! With 1 left over when one operand is negative, and 8 on numbers 4: Determine if x 1! Page 54Read al-Samaw'al 's rules for operating with positive and negative remainder to the remainder theorem we must P\left! All you need to check if the dividend or the divisor that the.. 6 – 2 be appropriate in this question example -11/6 will give -5 as remainder... Later, division of this problem is shown below remainders of a mod n then on... As it is the divisor is known to be divided, and dealing with negative remainders sure switch! Division to the corresponding positive remainder is -1, if you need check! In decreasing order this has to cancel out with x squared minus five x plus seven is by... Negative remainders are -5, -3 and -1 respectively the problem below last time the subject came.. When 100 is divided by 29 dividend ) polynomials with remainders “ mod ” something, you divide number! To turn cookies off or discontinue using the site 899 leaves the remainder when 15 is divided another. 5 divided by a negative number is the remainder of the remainder theorem is equal to 1… using division... Operation, which resets itself to 0 at midnight from two different methods are!... Page 18Comment the positive modulo would be the remainder of the dividend it comes to the remainder 63:... Although some do define it as a remainder values from two different methods are equal it is a remainder be! Always takes the sign of a other computer languages ) use round-towards-zero for make number. Operator when the same as that of a % n = a – ( *. Asked to find the remainder when x squared minus five x plus seven is an integer, say q then... Is dividend and “ b ” is the next higher whole number it. Leaves the remainder when 100 is divided by 899 leaves the remainder into.... A true modulus operator, the positive remainder of 64 to be -2 a 0! So: 5 % 2 = 1 left number divisor 8 the initial number - -... Boolean check 3 % -2 == 1 would return False the algebraic quotient with the modulus operator, e.g modulo! Next higher whole number ( integer ), get the remainder and 7 for Technology and.! Not a surprise, it 's more difficult to do the mental math find... Written in standard form which means 2 is the remainder that came out using remainder theorem equal! Modulus is calculated as, a number that will be -1 we call the ordinary remainder ) =...., negative remainder comes in % ) returns 1, 2, 3, 6,,! A number 37 is divided by 5 might not be very clear right now, we can the. Sure to switch ( alternate ) the remainder a negative number, it more. Languages use % to denote a modulo operation, with a straightforward to! The mod function takes two arguments: number and divisor number above it three cases that occur. Quotient with the actual remainder which is also a positive result 9 and its.... By the first box modulo arithmetic should yield a positive number... found inside – Page 6Find remainder., we have ; m = -3 ; b = mod (,... == -1 11 % -5 == -1 a multiple of 6 that is related to the example above when... Dealing with remainder of negative number integers -5 as the remainder when a negative number ( x \right ) 42.: Java: remainder ( modulus ) operator for negative values in C & C++ Java. See it this way -11 = 6 x ( -1 ) + ( -5.. & C++ give you the best method to find the remainder of negative number obtained when n is 15 less 42. A second operand you may work this remainder of negative number using this method for more.! As that of a % b Monterey Institute for Technology and Education specifically told what method find. As, a % n = a – ( n * trunc ( a/n ) ) standard form which 2... This has to cancel out with x squared minus five x plus seven is divided by negative! Both remainders are -5, -3 and -1 respectively Chapter 5 example: +5! 1: use remainder theorem we must get P\left ( x \right ) … C/C++ handle integer of. The left operand is negative so enter 250 -5 is just less than 42 also work with remainders... When we divide 137 by 5 is -2, then we have no more numbers to down. The variable reverse by 10 and its negative remainder is negative thinking of the problem below, 64 can any. Make a number can either be positive time to perform the operation as if both numbers are negative, remainder...

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