**Divisibility by 2**

A number is divisible by ‘2’ if it ends in zero or in a digit which is a multiple of ‘2’i.e. 2,4, 6, 8.

Example: 90,66

**Divisibility by 3**

A number is divisible by ‘3’, if the sum of the digits is divisible by ‘3’.

Example: 66.

6+6 = 12 = 1+2 =3**Divisibility by 4**

A number is divisible by ‘4’ if the number formed by the last two digits.

Example 6788

take 88 it is divisible by 4

**Divisibility by 5**

A number is divisible by ‘5’ if it ends in zero or 5

Example: 635, 980

**Divisibility by 6**

A number is divisible by ‘6’ if it divisible by ‘2’ as well as by ‘3’.

Example: 84.

4 is last digit so it is divisible by 2

8 + 4 = 12 = 1+2 = 3

**Divisibility by 7**

Subtract 2 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 7, the original number is also divisible by 7

Example: 784.

78- (4 *2) = 78-8 = 70 is divisible by 7

**Divisibility by 8**

A number is divisible by ‘8’ if the number formed by the last three digits, i.e,hundreds tens and units is divisible by ‘8’.

Example:9784

Consider 784

**Divisibility by 9**

A number is divisible by ‘9’ if the sum of its digit is divisible by ‘9’ or sum is equal to 9.

Example: 8973

8+9+7+3 = 27 = 2+ 7 =9

**Divisibility by 10**

A number is divisible by ‘10’ if it ends in zero.

Example: 60,780

**Divisibility by 11**

A number is divisible by ‘11’ if the difference between the sums of the digits in the even and odd places is zero or a multiple of ‘11’

3729 = ( (7+9) – (2+3)) = (16 – 5) = 11 so OK

**Divisibility by 12**

A number is divisible by 12 if it is divisible by both 4 and 3.

Example: 1212

1+2+1+2= 6 is divisible by 3

12 is divisible by 4

**Divisibility by 13 **

Add 4 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 13, the original number is also divisible by 13.

Example: 169 is divisible by 13

9 * 4 = 36.

36 + 16 = 52 which is divisible by 13

**Divisibility by 14**

If a number is divisible by 2 as well as 7.

Example 784.

4 is divisible by 2.

78- (4 *2) = 78-8 = 70 is divisible by 7

**Divisibility by 15**

If a number is divisible by both 3 & 5.

Example is 225.

2+2+5 = 9 is divisible by 3

**Divisibility by 17 **

Subtract 5 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 17, the original number is also divisible by 17.

**Divisibility by 18**

If a number is divisible by both 2 & 9.

108 is divisible by 18.

1+0+8 = 9 is divisible by 9.

8 is divisible by 2**Divisibility by 19**

Add 2 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 19, the original number is also divisible by 19.

Example: 95.

9 + (2 * 5) = 19 is divisible by 19

**Divisibility by 21**

If a number is divisible by both 3 & 7.

Example is 84

**Divisibility by 23 **

Add 7 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 23, the original number is also divisible by 23.

Example is 115.

11+(7*5) = 46**Divisibility by 24**

If a number is divisible by both 3 & 8.

**Divisibility by 29 **

Add 3 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 29, the original number is also divisible by 29. **Divisibility by 31**

Subtract 3 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 31, the original number is also divisible by 31

Check for 49507 =4950-(3*7)=4929 =492-(3*9) =465 =46-(3*5)=31. Hence 49507 is divisible by 31.