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The Modulus is the remainder of the euclidean division of one number by another. % is called the modulo operation. For instance, 9 divided by 4 equals 2 but it remains 1. Here, 9 / 4 = 2 and 9 % 4 = 1. In your example: 5 divided by 7 gives 0 but it remains 5 (5 % 7 == 5). Calculation.
The modulo (or "modulus" or "mod") is the remainder after dividing one number by another. Example: 100 mod 9 equals 1. Because 100 9 = 11 with a remainder of 1.
How It Works. The modulus operator - or more precisely, the modulo operation - is a way to determine the remainder of a division operation. Instead of returning the result of the division, the modulo operation returns the whole number remainder.
Definition: Modulo. Let \(m\) \(\in\) \(\mathbb{Z_+}\). \(a\) is congruent to \(b\) modulo \(m\) denoted as \( a \equiv b (mod \, n) \), if \(a\) and \(b\) have the remainder when they are divided by \(n\), for \(a, b \in \mathbb{Z}\).
When you see "modulo", especially if you are using a calculator, think of it as the remainder term when you do division. Examples: The result of 10 modulo 5 is 0 because the remainder of 10 / 5 is 0. The result of 7 modulo 5 is 2 because the remainder of 7 / 5 is 2.
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]
How to Do a Modulo Calculation. The modulo operation finds the remainder of a divided by b. To do this by hand just divide two numbers and note the remainder. If you needed to find 27 mod 6, divide 27 by 6. 27 mod 6 = ? 27 ÷ 6 = 4 with a remainder of 3. 27 mod 6 = 3. Example Modulo Calculation.