# Divisibility Rules

1. A number will be divisible by 2 iff the digit at the unit place is divisible by 2.

2. A number will be divisible by 3 iff the sum of digits of the number is divisible by 3

3. A number will be divisible by 4 iff last two digits of the number together are divisible by 4.

4. A number will be divisible by 5 iff digit at the unit place is either 0 or 5.

5. A number will be divisible by 6 iff the digit at the unit place of the number is divisible by 2 & sum of all digits of the number is divisible by 3.

6. Divisibility test of 7: Make two set of three nos. starts from unit digit then add the alternate sets, and find out the mutual difference, if it is 0 or any multiple of 7 then the given no. is divisible by 7.

e.g.,   001234567

567  + 001 – 234 = 334

Since 334 is not divisible by 7 the given no. is also not divisible by 7.

The same test is applicable for 11 & 13. In these cases we have to see the result is divisible by 11 or 13 respectively or not.

1. A number will be divisible by 8 iff the last 3 digits, all together, is divisible by 8.

2. A number will be divisible by 9 iff sum of all it’s digits is divisible by 9.

3. A number will be divisible by 10 iff it’s last digit is 0.

4. A number will be divisible by 11, iff the difference between the sum of the digits at even places and sum of the digits at odd places is a multiple of 11.

e.g., 1298, 1221, 123321, 12344321, 1234554321, 123456654321, 795432

1. Divisibility By 12: A number is divisible by 12, if it is divisible by both 4 and 3.

2. Divisibility By 14: A number is divisible by 14, if it is divisible by 2 as well as 7.

3. Divisibility By 15: A number is divisible by 15, if it is divisible by both 3 and 5.

4. Divisibility by 16: A number is divisible by 16, if the number formed by the last 4 digits is divisible by 16.

5. Divisibility by 24: A given number is divisible by 24, if it is divisible by both 3 and 8.

6. Divisibility by 40: A given number is divisible by 40, if it is divisible by both 5 and 8.

7. Divisibility by 80: A given number is divisible by 80, if it is divisible by both 5 and 16.

If a number is divisible by p as well as q, where p and q are co-primes, then the given number is divisible by pq.

If p and q are not co-primes, then the given number need not be divisible by pq, even when it is divisible by both p and q.