**Divisibility by 2**

**:**If last digit of the number is even i.e. 0,2,4,6,8

Ex : 876999578 is divisible by 2.

**Divisibility by 3:**If the sum of digits is divisible by 3.

Ex: 327 is divisible by 3, since sum of its digits = (3+2+7) = 12 , which is divisible by 3.

**Divisibility by 4:**If the last two digits of the number is divisible by 4

Ex: 2648 is divisible by 4, since the number formed by the last two digits is 48 which is divisible by 4.

**Divisibility by 5:**If the last digit of the number ends with 0 or 5.

Ex: 20870 ends in a 0, so it is divisible by 5.

**Divisibility by 6:**If the number is divisible by both 2 & 3.

Ex: 558 is divisible by 6, because it is divisible by 2(number is even) as well as 3 (5+5+8=18,which is divisible by 3).

Divisibility by 7: Multiply the last digit by 5 and add the product to the remaining truncated number. Continue doing these steps until you reach a 2 digit number.

If the result is divisible by 7, we say that the original dividend is divisible by 7.

Example: 33803--> 3380+(3*5)=3380+15=3395 -->339+(5*5)=339+25 = 364 --> 36+(4*5)=36+20=56 (since this number is divisible by 7, you can say 3185 is also divisible by 7)

* There are many more approaches to check the divisibility by 7.

**Divisibility by 8:**If the last three digits of the number are divisible by 8.

Ex: 3652736 is divisible by 8 because last three digits (736) is divisible by 8.

**Note:**Rule of divisibility by 2 & 4 on the last three digit number will not be applicable here. You have to check the divisibility manually.

Ex: 516 is divisible by 2 & 4 but not by 8.

**Divisibility by 9:**If the sum of the digits is divisible by 9.

Ex: 672381 is divisible by 9, since sum of digits = (6+7+2+3+8+1) = 27 is divisible by 9.

**Divisibility by 10:**If the digit at units place is 0 it is divisible by 10.

Ex: 697420, 243540 is divisible by 10.

**Divisibility by 11:**If the difference of 'sum of its digits at odd places' and 'sum of its digits at even places' is either 0 or a number divisible by 11.

Ex: 4832718 is divisible by 11, since:

(Sum of digits at odd places) and (sum of digits at even places)

= (8+7+3+4)-(1+2+8) = 11

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

Ex: 34632

(i) The number formed by last two digits is 32, which is divisible by 4

(ii) Sum of digits = (3+4+6+2) = 18, which is divisible by 3.

**Divisibility by 13:**Multiply the last digit by 4 and add the product to the remaining truncated number. Continue doing these steps until you reach a 2 digit number.

If the result is divisible by 13, we say that the original dividend is divisible by 13.

Example: 3185--> 318+(5*4)=318+20=338 -->33+(8*4)=33+32 = 65 (since this number is divisible by 13, you can say 3185 is also divisible by 13)

**Divisibility by 14:**If a number is divisible by both 2 & 7.

**Divisibility by 15:**If a number is divisible by both 3 & 5.

**TIP:**If a number is divisible by two different prime numbers, then it is divisible by the products of those two numbers.

Ex: 30 is divisible by both 3 and 5, it is also divisible by 15.