# Divisibility Rules

Once your kids have mastered their division facts, it’s always good to teach them the divisibility rules. These rules can help them determine if a number is divisible by another number evenly without performing actual division. They can come handy when learning about factors and doing long divisions under a time constrain. This helps our kids to look at large numbers with greater ease and builds their number sense.

There is also a divisibility rules poster for numbers 2-9 at the end of the post to print so that your kids can practice them or to keep it in their math journal.

**Divisibility by 2**

A number is divisible by 2 if its an even number ie last digit is either 0,2,4,6,8.

For example, The number 5678 is divisible by 2 because the last digit is 8.

**Divisibility by 3**

A number is divisible by 3, if sum of all its digits is divisible by 3.

For example, The number 6417 is divisible by 3 because 6+4+7+1 = 18 which is divisible by 3

**Divisibility by 4**

A number is divisible by 4 if its last two digits are divisible by 4.

For example, The number 9412 is divisible by 4 because the last two digits ie 12 is divisible by 4.

**Divisibility by 5**

A number is divisible by 5 if the last digit is 0 or 5.

For example, The number 7215 is divisible by 5 because the last digit is 5.

**Divisibility by 6**

If the number is divisible by both 2 and 3, then the number is divisible by 6.

For example, The number 7116 is an even number (divisible by 2 ) and also 7+1+1+6 = 15 which is divisible by 3. So, the number is divisible by 6

**Divisibility by 7**

A number is divisible by 7 , if

- Take the last digit and double it.
- Subtract this number from the remaining number
- If the resulting number is divisible by 7 or is 0 then the entire number is divisible by 7

For example, The number 7119 is divisible by 7 because 9 +9 = 18 ( double the last digit ) and 711 – 18 = 693 . We can apply the divisibility rule of 7 again on the number 693 until we find a number smaller enough to determine if it’s divisible by 7. So, applying the rule on 693, we have 3+3 = 6 and 69 – 6 = 63 which is divisible by 7 . Hence, the number 7119 is divisible by 7.

**Divisibility by 8**

A number is divisible by 8 if its last 3 digits are divisible by 8.

For example, The number 9112 is divisible by 8 because 112 ( last three digits) is divisible by 8.

**Divisibility by 9**

A number is divisible by 9 if sum of all its digit is divisible by 9.

For example, The number 6543 is divisible by 9 because the 6+5+4+3 = 18 which is divisible by 9.

**Divisibility by 10**

If the last digit of the number is 0, then the number is divisible by 10.

For example, The number 8980 is divisible by 10 because the last digit is 0.

**Divisibility by 1**1

There are two divisibility rules for number 11

– If by subtracting the last digit from the remaining digits results in a number divisible by 11.**Rule 1**– A number is divisible by 11 if by subtracting the sum of its digits in the even numbered places from the sum of its digits in the odd numbered places ( or vice versa ) results in a number which is divisible by 11 or is 0, then the number is divisible by 11.*Rule 2*

For example, the number 913 is divisible by 11 because 91-3 = 88 (rule 1) which is divisible by 11.

The number 1364 is divisible by 11 because 1+6 – 3 – 4 = 0 (rule 2) is 0 .

**Divisibility by 12**

If the number is divisible by both 3 and 4, then the number is divisible by 12.

For example, the number 648 is divisible by 3 ( 6+4 + 8 = 18 divisible by 3 rule ) and by 4 (48 is divisible by 4, divisibility by 4 rule ) , therefore it is divisible by 12.

**Divisibility by 13**

If by multiplying the last digit of a number with 9 and subtracting it from the rest of the number, results in a number which is divisible by 13 or is 0 then the number is divisible by 13.

For example, for the number 247 , multiply the last digit with 9 gives 7*9 = 63 . Subtracting it from remaining number gives ( 24 – 63 = -39 ) which is divisible by 13 so the whole number is divisible by 13.

**Divisibility by 14**

A number is divisible by 14, if the number is divisible by 2 and 7.

For example, the number 1204 is even ( divisible by 2 ) and 120 – 8 = 112 ( divisible by 7 ) so the number is divisible by 14

**Divisibility by 15**

A number is divisible by 15, if the number is divisible by 3 and 5.

For example, the number 2415 is divisible by 3 ( because 2+4+1+5 = 12 which is divisible by 3 ) and the last digit is 5 so it is divisible by 15.

Feel free to download the poster and practice them with your kids. If you like reading my blog, please consider following it. Thank you !