# Divisibility Rules

Divisibility rules were used by almost everyone before calculators were invented. They are useful today because using them can save you a lot of time.

 A number is divisible by the number if: 2 the last digit of the number is even: 0, 2, 4, 6, or 8 1234 is divisible by 2 because it ends in 4 2345 is not divisible by 2 because it ends in 5 3 the sum of the digits is divisible by 3 (with no remainder) 1234 is not divisible by 3 because 1 + 2 + 3 + 4 = 10 2345 is not divisible by 3 because 2 + 3 + 4 + 5 = 14 3345 is divisible by 3 because 3 + 3 + 4 + 5 = 15 4 the last two digits in the number is divisible by 4 (with no remainder) 1234 is not divisible by 4 because 34 is not divisible by 4 2345 is not divisible by 4 because 45 is not divisible by 4 3960 is divisible by 4 because 60 is divisible by 4 5 the last digit of the number is 0 or 5 1234 is not divisible by 5 because it ends in 4 2345 is divisible by 5 because it ends in 5 6 it is divisible by both 2 and 3 – use the rules above for 2 and 3 2345 is not divisible by 6 because it is not divisible by 2 3960 is divisible by 6 because it ends in 0 (divisible by 2) and the sum of the digits is 18 (divisible by 3) 8 if the last three digits are divisible by 8 (with no remainder) 1234 is not divisible by 8 because 234 is not divisible by 8 3960 is divisible by 8 because 960 is divisible by 8 9 the sum of the digits is divisible by 9 3345 is not divisible by 9 because 3 + 3 + 4 + 5 = 15 1233 is divisible by 9 because 1 + 2 + 3 + 3 = 9 10 if the number ends in 0 11 if the sums of the alternate digits are different by 0, 11, 22, or 33, or any two-digit multiple of 11. In other words, say you have a six-digit number: Add up the first, third, fifth digits – the odd ones. Then add the digits in the even places – second, fourth, sixth. Then subtract those totals from each other, and if the answer is a multiple of 11, the original number is divisible by 11. 3960 is divisible by 11 because 3 + 6 and 9 + 0 both add up to 9, so the difference is 0, which is a multiple of 11 ( 0 • 11)

Comments, questions, or you just need some help? Send an e-mail to Mrs. Shearer Last Updated: 11/24/2005
© K. A. Shearer 2005-2009

Buttons created at ButtonGenerator.com.