Divisibility Rules!

To find if some number X is divisible by prime numbers, 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 5	If the last digit is 5 or 0, then X is divisible by 5
By 7	The last digit of X times 2 and subtract it from X without its last digit. For instance, if the number X you are testing is 345678, 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 7.
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 13	The last digit of X times 4 and add it from X without its last digit. For instance, if the number X you are testing is 345678, 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 13.
By 17	The last digit of X times 5 and subtract it from X without its last digit. For instance, if the number X you are testing is 345678, you would subtract 40 from 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 17.
By 19	The last digit of X times 2 and add it from X without its last digit. For instance, if the number X you are testing is 345678, you would add 16 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 19.
By 23	The last digit of X times 7 and add it from X without its last digit. For instance, if the number X you are testing is 345678, you would add 52 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 23.
By 29	The last digit of X times 3 and add it from X without its last digit. For instance, if the number X you are testing is 345678, you would add 24 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 29.
By 31	The last digit of X times 3 and substract it from X without its last digit. For instance, if the number X you are testing is 345678, you would substract 24 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 31.
By 37	The last digit of X times 11 and subtract it from X without its last digit. For instance, if the number X you are testing is 345678, you would subtract 88 from 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 37.
By 41	The last digit of X times 4 and substract it from X without its last digit. For instance, if the number X you are testing is 345678, you would substract 32 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 41.
By 43	The last digit of X times 11 and add it from X without its last digit. For instance, if the number X you are testing is 345678, you would add 88 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 43.
By 47	The last digit of X times 14 and subtract it from X without its last digit. For instance, if the number X you are testing is 345678, you would subtract 112 from 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 47.
By 53	The last digit of X times 16 and add it from X without its last digit. For instance, if the number X you are testing is 345678, you would add 128 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 53.
By 59	The last digit of X tmes 6 and add it from X without its last digit. For instance, if the number X you are testing is 345678, you would add 54 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 59.
By 61	The last digit of X times 6 and substract it from X without its last digit. For instance, if the number X you are testing is 345678, you would substract 48 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 61.
By 67	The last digit of X times 20 and subtract it from X without its last digit. For instance, if the number X you are testing is 345678, you would subtract 160 from 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 67.
By 71	The last digit of X times 7 and substract it from X without its last digit. For instance, if the number X you are testing is 345678, you would substract 56 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 71.
By 73	The last digit of X times 22 and add it from X without its last digit. For instance, if the number X you are testing is 345678, you would add 176 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 73.
By 79	The last digit of X tmes 8 and add it from X without its last digit. For instance, if the number X you are testing is 345678, you would add 64 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 79.
By 83	The last digit of X times 7 and add it from X without its last digit. For instance, if the number X you are testing is345678, you would add 52 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 83.
By 89	The last digit of X tmes 9 and add it from X without its last digit. For instance, if the number X you are testing is 345678, you would add 72 to 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 89.
By 97	The last digit of X times 29 and subtract it from X without its last digit. For instance, if the number X you are testing is 345678, you would subtract 232 from 34567. Repeat this procedure until you get a number that you know for sure is or is not divisible by 97.