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For algorithms describing how to calculate the remainder, see Division algorithm.) The remainder, as defined above, is called the least positive remainder or simply the remainder . [ 2 ] The integer a is either a multiple of d , or lies in the interval between consecutive multiples of d , namely, q ⋅ d and ( q + 1) d (for positive q ).
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. [1]
To calculate the check digit, take the remainder of (53 / 10), which is also known as (53 modulo 10), and if not 0, subtract from 10. Therefore, the check digit value is 7. i.e. (53 / 10) = 5 remainder 3; 10 - 3 = 7. Another example: to calculate the check digit for the following food item "01010101010x". Add the odd number digits: 0+0+0+0+0+0 = 0.
Formulas in the B column multiply values from the A column using relative references, and the formula in B4 uses the SUM() function to find the sum of values in the B1:B3 range. A formula identifies the calculation needed to place the result in the cell it is contained within. A cell containing a formula, therefore, has two display components ...
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.
The congruence relation, modulo m, partitions the set of integers into m congruence classes. Operations of addition and multiplication can be defined on these m objects in the following way: To either add or multiply two congruence classes, first pick a representative (in any way) from each class, then perform the usual operation for integers on the two representatives and finally take the ...
It is based on modular arithmetic modulo 9, and specifically on the crucial property that 10 ≡ 1 (mod 9). Arithmetic modulo 7 is used in algorithms that determine the day of the week for a given date. In particular, Zeller's congruence and the Doomsday algorithm make heavy use of modulo-7 arithmetic.
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. For example, given b = 5, e = 3 and m = 13, dividing 5 3 = 125 by 13 leaves a remainder of c = 8.
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