Divisibility Formulas and Properties

June 23, 2019

Firstly you must know these rules by heart –

Divisibility by 2 – If the units digit of the number is even like 2, 4, 6, 8, 0 then the number is divisible by 2.
Divisibility by 3 – If the sum of digits of number is divisible by 3 then number is divisible by 3. e.g. 342 = 3 + 4 + 2 = 9. Now, 9 is divisible by 3 thus 342 is divisible by 3
Divisibility by 4 – If last two digits are multiples of 4. e.g. 1048 is divisible by 4 as 48 is divisible by 4 since, 4×12 =48.
- Thus, 89872394870198712316 is divisible by 4, since 16 is divisible by 4
Divisibility by 5 – If last two digits are either 0 or 5.
Divisibility by 6 – It should be even and also be divisible by 3.
Divisibility by 7 – If you subtract the unit digit twice from the remaining digits of the Number(N) and the result is multiple of 7 then the number N is divisible by 7. e.g. – 665 is divisible by 7 as 66 – 10 = 56. Now, 56 is divisible by 7 so number 665 is divisible by 7.
Divisible by 8 – If the last 3 digits of the number are multiple of 8. eg 682878488 is divisible by 8 as 488 is divisible by 8.
Divisible by 9 – If the sum of digits of a number Nis a multiple of 9
Divisible by 11 – If the difference of the alternating sum of digits of a number N, is a multiple of 11 (e.g. 2343 is divisible by 11 because, 2 – 3 + 4 – 3 = 0, which is a multiple of 11)