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In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
In the second step, any natural number c that divides both a and b (in other words, any common divisor of a and b) divides the remainders r k. By definition, a and b can be written as multiples of c: a = mc and b = nc, where m and n are natural numbers. Therefore, c divides the initial remainder r 0, since r 0 = a − q 0 b = mc − q 0 nc = (m ...
The operation consisting of computing only the remainder is called the modulo operation, [3] and is used often in both mathematics and computer science. The pie has 9 slices, so each of the 4 people receives 2 slices and 1 is left over.
Before C99, the C language allowed other choices.) Perl, Python (only modern versions) choose the remainder with the same sign as the divisor d. [6] Scheme offer two functions, remainder and modulo – Ada and PL/I have mod and rem, while Fortran has mod and modulo; in each case, the former agrees in sign with the dividend, and the latter with ...
Then one can proceed by adding 20 = 5 × 4 at each step, and computing only the remainders by 3. This gives 4 mod 4 → 0. Continue 4 + 5 = 9 mod 4 →1. Continue 9 + 5 = 14 mod 4 → 2. Continue 14 + 5 = 19 mod 4 → 3. OK, continue by considering remainders modulo 3 and adding 5 × 4 = 20 each time 19 mod 3 → 1. Continue 19 + 20 = 39 mod 3 ...
Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = b e mod m. From the definition of division, it follows that 0 ≤ c < m .
One must multiply the leftmost digit of the original number by 3, add the next digit, take the remainder when divided by 7, and continue from the beginning: multiply by 3, add the next digit, etc. For example, the number 371: 3×3 + 7 = 16 remainder 2, and 2×3 + 1 = 7. This method can be used to find the remainder of division by 7.