Fast Math Rules for Divisibility -- Summary

Divisible by 2 : Right-most (one's) digit is even.

Divisible by 3 : Sum of the digits of the number is divisible by 3.

Divisible by 4 : Right-most 2 digits (taken together) are divisible by 4.

Divisible by 5 : Right-most (one's) digit is 0 or 5.

Divisible by 6 : Number is divisible by 2 AND divisible by 3.

Divisible by 7 : Break up number into groups of 3 digits, starting from the right. Add up every other group of digits to form a sum. Add up the remaining groups of digits to form a second sum. Find the difference between the two sums. If that difference is divisible by 7, so is the original number.

Divisible by 8 : Right-most 3 digits (taken together) are divisible by 8.

Divisible by 9 : Sum of the digits of the number is divisible by 9.

Divisible by 10 : Right-most (one's) digit is a 0.

Divisible by 11 :

Method 1 : Add up every other digit, starting from the left-most digit, to form a sum. Add up the remaining digits to form a second sum. Find the difference between the two sums. If that difference is divisible by 11, so is the original number.

Method 2 : Break up number into groups of 3 digits, starting from the right. Add up every other group of digits to form a sum. Add up the remaining groups of digits to form a second sum. Find the difference between the two sums. If that difference is divisible by 11, so is the original number.

Divisible by 12 : Number is divisible by 3 AND divisible by 4.

Divisible by 13 : Break up number into groups of 3 digits, starting from the right. Add up every other group of digits to form a sum. Add up the remaining groups of digits to form a second sum. Find the difference between the two sums. If that difference is divisible by 13, so is the original number.

Divisible by 14 : Number is divisible by 2 AND divisible by 7.

Divisible by 15 : Number is divisible by 3 AND divisible by 5.

Divisible by 16 : Right-most 4 digits (taken together) are divisible by 16.

divisibility rule summary.doc 10/26/06

Divisible by 18 : Number is divisible by 2 AND divisible by 9.

Divisible by 20 :

Method 1: Number is divisible by 4 AND divisible by 5.

Method 2 : One’s digit is “0” and ten’s digit is even.

Method 3 : Number ends in 00, 20, 40, 60, 80

Divisible by 21 : Number is divisible by 3 AND divisible by 7.

Divisible by 22 : Number is divisible by 2 AND divisible by 11.

Divisible by 24 : Number is divisible by 3 AND divisible by 8.

Divisible by 25 : Right-most 2 digits are divisible by 25.

Divisible by 26 : Number is divisible by 2 AND divisible by 13.

Divisible by 27 : First check if number is divisible by 9. If so, divide the number by 3. If quotient is divisible by 9, so is the original number.

Divisible by 28 : Number is divisible by 4 AND divisible by 7.

Divisible by 30 : Method 1 : Number is divisible by 2 AND divisible by 3 AND divisible by 5.

Method 2 : Number ends in “0” AND is divisible by 3.

Divisible by 32 : Right-most 5 digits (taken together) are divisible by 32.

Divisible by 33: Number is divisible by both 3 and 11.

Divisible by 64, 128, and higher powers of 2 : Following the pattern of divisibility by 2, 4, 8, 16, and 32 (1st, 2nd, 3rd, 4th, and 5th powers of 2) -- take the right-most "n" digits of the number, where "n" is the power of 2. If that group of digits is divisible, so is the original number.

divisibility rule summary.doc 10/26/06