Divisibility Rules

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
By17*	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
By19*	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...