# Divisibility Rules!

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## Divisibility Rules!

To find if some number X is divisible by a certain number, test the number by using the information in the table below.

By 2 If the last digit divisible by two, then X is too

By 3 If the sum of the digits of the number X is divisible by three, then X is too

By 4 If the last two digits are divisible by four, then X is too

By 5 If the last digit is 5 or 0, then X is divisible by 5

By 6 If X is divisible by 2 and by 3, then X is divisible by 6

By 7 This rule is called L-2M. What you do is to double the last digit of the number X and subtract it from X without its last digit. For instance, if the number X you are testing is345678, you would subtract 16 from 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by seven. Then the X's divisibility will be the same.

By 8 If the last three digits are divisible by 8, then X is too

By 9 If the sum of the digits of the number X is divisible by nine, then X is too

By 10 If the last digit of X is 0, then X is divisible by 10

By 11 What you do here is to make two sums of digits and subtract them. The first sum is the sum of the first, third, fifth, seventh, etc. digits and the other sum is the sum of the second, fourth, sixth, eighth, etc. digits. If, when you subtract the sums from each other, the difference is divisible by 11, then the number X is too

By 12 If X is divisible by 4 and by 3, then X is divisible by 12

By 13 This rule is called L+4M. What you do is to quadruple the last digit of the number X and add it from X without its last digit. For instance, if the number X you are testing is345678, you would add 32 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by thirteen. Then the X's divisibility will be the same.

By 14 If X is divisible by 7 and by 2, then X is divisible by 14

By 15 If X is divisible by 5 and by 3, then X is divisible by 15

By 16 If the last four digits are divisible by 16, then X is too

By 17* This rule is called L-5M. See rules for 7 and 13 on how to apply.

By 18 If X is divisible by 9 and by 2, then X is divisible by 18

By 19* This rule is called L+2M. See rules for 7 and 13 on how to apply.

By 20 If X is divisible by 5 and by 4, then X is divisible by 20

By 21 If X is divisible by 7 and by 3, then X is divisible by 21

By 22 If X is divisible by 11 and by 2, then X is divisible by 22

By 24 If X is divisible by 8 and by 3, then X is divisible by 24

By 25 If the last two digits of X are divisible by 25, then X is too

Higher You can use multiple rules for multiple divisors...for instance, to check if a number is divisible by 57, check to see if it is divisible by 19 and 3, etc., since 57 = 19 x 3...

By 2 If the last digit divisible by two, then X is too

By 3 If the sum of the digits of the number X is divisible by three, then X is too

By 4 If the last two digits are divisible by four, then X is too

By 5 If the last digit is 5 or 0, then X is divisible by 5

By 6 If X is divisible by 2 and by 3, then X is divisible by 6

By 7 This rule is called L-2M. What you do is to double the last digit of the number X and subtract it from X without its last digit. For instance, if the number X you are testing is345678, you would subtract 16 from 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by seven. Then the X's divisibility will be the same.

By 8 If the last three digits are divisible by 8, then X is too

By 9 If the sum of the digits of the number X is divisible by nine, then X is too

By 10 If the last digit of X is 0, then X is divisible by 10

By 11 What you do here is to make two sums of digits and subtract them. The first sum is the sum of the first, third, fifth, seventh, etc. digits and the other sum is the sum of the second, fourth, sixth, eighth, etc. digits. If, when you subtract the sums from each other, the difference is divisible by 11, then the number X is too

By 12 If X is divisible by 4 and by 3, then X is divisible by 12

By 13 This rule is called L+4M. What you do is to quadruple the last digit of the number X and add it from X without its last digit. For instance, if the number X you are testing is345678, you would add 32 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by thirteen. Then the X's divisibility will be the same.

By 14 If X is divisible by 7 and by 2, then X is divisible by 14

By 15 If X is divisible by 5 and by 3, then X is divisible by 15

By 16 If the last four digits are divisible by 16, then X is too

By 17* This rule is called L-5M. See rules for 7 and 13 on how to apply.

By 18 If X is divisible by 9 and by 2, then X is divisible by 18

By 19* This rule is called L+2M. See rules for 7 and 13 on how to apply.

By 20 If X is divisible by 5 and by 4, then X is divisible by 20

By 21 If X is divisible by 7 and by 3, then X is divisible by 21

By 22 If X is divisible by 11 and by 2, then X is divisible by 22

By 24 If X is divisible by 8 and by 3, then X is divisible by 24

By 25 If the last two digits of X are divisible by 25, then X is too

Higher You can use multiple rules for multiple divisors...for instance, to check if a number is divisible by 57, check to see if it is divisible by 19 and 3, etc., since 57 = 19 x 3...

**HighTec**- Posts : 49

Join date : 2007-11-17

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