A divided by B = Quotient Q times B plus Remainder R

For example:

Sometimes, we are only interested in what the remainder is when we divide A by B. For these cases, we usually use an operator called the modulo operator (abbreviated as mod).

12 mod 5 = 6

25 mod 4 = 1

12 mod 6 = 0

Practices:

34 mod 7 = ?

121 mod 49 = ?

50 mod 3 = ?

The following materials are intended only for students of Grades 7 and 8 or above.

Congruence

Congruence is an important and useful tool for the study of divisibility. We have the following definition:

If A and B are integers and, and n is a positive integer, then

Which is read as: A is congruent to B modulo (or mod) n, and it means that B - A is divisible by n.

For example, we have:

We also have the following theorem:

For any integers A, B and C, and positive integer n: