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.
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