### Divisibility Rules By 2, 3, 4, 5, 6, 8, and 11

Divisible by 2, 4, 8

• A number would be divisible by 2 if the last is divisible by 2.
For Example - 12, Here the last digit is 2, and 2 is divisible by 2 so 12 is divisible by 2.

273, Here the last digit is 3 so it is NOT divisible by 2.
• A number would be divisible by 4 if the last 2 digits are divisible by 4.
For Example - 312, Here the last two digits are 12, and 12 is divisible by 4 so 312 is divisible by 4.

3457, Here the last two digits are 57, and 57 is NOT divisible by 4.

• A number would be divisible by 8 if the last 3 digits are divisible by 4.
For Example - 114, Here the last 3 digits are 114 itself and it is divisible by 8.

Note: 2^(k) = N, A number would be divisible by N if the last k digit of that number is divisible by N.

Similarly,

2^(1) = 2, A number is divisible by 2 if the last 1 digit of that number is divisible by 2.
2^(2) = 4, A number is divisible by 4 if the last 2 digit of that number is divisible by 4.
2^(3) = 8, A number is divisible by 8 if the last 3 digit of that number is divisible by 8.

### Divisible by 3, 5, 6

• A number would be divisible by 3 if the sum of digits of that number is divisible by 3.
For Example - 567, Sum of digits of 567 is 18 and it is divisible by 3, so 567 is divisible by 3.

3402, Sum of digits of 3402 is 9 and it is divisible by 3, so 3402 is divisible by 3.
• A number would be divisible by 5 if the last digit of it is 0 or 5.
For Example - 3445, is divisible by 5.

45670, is divisible by 5.

5003, is NOT divisible by 5.
• A number would be divisible by 6 if it is divisible by 2 and 3 both (We already know to check the divisibility by 2 and 3).
For Example - 156 is divisible by 2 and 3 both (Divisible by 6).
258 is divisible by 2 and 3 both (Divisible by 6).

### Divisible by 11

• Take the alternating sum of digits reading from left to right and find their difference. If the difference is divisible then the number is also divisible by 11.
It is very easy to say the divisibility of numbers like 44, 55, 7777 is divisible by 11. But when the number looks like 10824, 10813 then the above rule will help.

For Example - 10824

Sum of digit at odd places = 1 + 8 + 4 = 13

Sum of digit at even places = 0 + 2 = 2

Difference = 13 - 2 = 11 and it is divisible by 11 (10824 is Divisible by 11).

Written with 💗 by Manish