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.

● Divisibility Rules.

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.

5th Grade Math Problems

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