# 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 11

There are two divisibility rules for number 11

• Rule 1 – If by subtracting the last digit from the remaining digits results in a number divisible by 11.
• Rule 2 – 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.

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.