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

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