# Properties of Divisibility

We will discuss here about what are the properties of divisibility.

The following properties are:

(i) When a number is divisible by another number, it is also divisible by the factors of the number.

For example, 48 is divisible by 12

And 12 = 2 × 3 × 4, so 2, 3 and 4 are the factors of 12.

Therefore 48 is also divisible by 2, 3 and 4

i.e. 48 ÷ 2 = 24, 48 ÷ 3 = 16 and 48 ÷ 4 = 12

(ii) When a number is divisible by two or more co-prime numbers, it is also divisible by their products.

For example, 12 is divisible by 2 and 3 as,

12 ÷ 2 = 6 and 12 ÷ 3 = 4

The product of 2 and 3 = 2 × 3 = 6

Therefore, 12 is also divisible by 6 i.e., 12 ÷ 6 = 2.

(iii) When a number is a factor of two given numbers, it is also a factor of their sum and difference.

For example, 6 is a factor of 18 since 18 ÷ 6 = 3

6 is a factor of 30 since 30 ÷ 6 = 5

Also, 6 is a factor of (30 + 18) = 48 since, 48 ÷ 6 = 8.

Also, 6 is a factor of (30 - 18) = 12 since, 12 ÷ 6 =2.

(iv) When a number is a factor of another number, it is also a factor of any multiple of that number.

For example, 4 is a factor of 12 since, 12 = 4 × 3.

Also, 108 is multiple of 12 as 108 = 9 × 12.

Therefore, 12 is also factor of 108 since 108 = 4 × 27.

Divisible by 2.

Divisible by 3.

Divisible by 4.

Divisible by 5.

Divisible by 6.

Divisible by 7.

Divisible by 8.

Divisible by 9.

Divisible by 10.

Divisible by 11.

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