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Definition of divisibility in math

What is divisibility in math? What is the meaning of divisibility in math?

Define divisibility in math

The definition of divisibility in mathematics:

Given an integer a and an integer b.
a is divisible by b if there is an integer k such that b * k = a.

So

a ÷ b = k

k is an integer.

It is said that

b is a divisor of a

a is divisible by b

Divisibility examples

4 examples of divisibility.

Example of divisibility

8 ÷ 4 = 2
4 * 2 = 8

The quotient 2 is an integer. Thus, we say that the integer 8 is exactly divisible by 4.

4 is a divisor of 8.

Example of divisibility

10 ÷ 4 = 2.5

The quotient 2.5 is not an integer. Thus, we say that the integer 10 is not exactly divisible by 4.

4 is not a divisor of 10.

Example of divisibility

22 ÷ 11 = 2

The quotient 2 is an integer. Thus, we say that the integer 22 is exactly divisible by 11.

11 is a divisor of 22.

Example of divisibility

150 ÷ 25 = 6

The quotient 6 is an integer. Thus, we say that the integer 150 is exactly divisible by 25.

25 is a divisor of 150.