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:
