Divisibility Rules

For a number to be divisible by another number means that when you divide the two numbers, the resulting quotient is a whole number.

Divisibility Rules

These rules allow us to determine if one number is divisible by another number without having to actually divide. It is a quick test and can save time when attempting to solve various math problems.

By applying the following rules, you easily determine the least common denominator when working with fractions as well.

Rule for 2

Any number is divisible by 2 if the number being divided is an even number (it must end in 0,2,4,6,8)

176  (ends with 8) Yes

85 (ends in 5 not an even number) No

Rule for 3

Any number is divisible by 3 if the sum of the number’s digits is divisible by 3.

351 Yes   3+5+1 = 9 (9 is a multiple of 3)

728 No 7+2+8 = 17 ( 17 is NOT a multiple of 3)

Rule for 4

Any number is divisible by 4 if the last 2 digits are divisible by 4 or the number ends in 00.

7712 Yes (12 is a multiple of 4)

922 No (22 is NOT a multiple of 4)

700 Yes (last two digits are 00)

Rule for 5

Any number is divisible by 6 if the number ends in 5 or 0

345 Yes  (ends in 5)

70 Yes (ends in 0)

851 No (does not end in 0 or 5)

Rule for 6

Any number is divisible by 6 if it is divisible by 2 and 3. In other words, the number must be an even number and the sum of its digits must be divisible by 3.

636 Yes (even, digits = 15, 6+3+6 = 15 which is divisible by 3, divisible by 2,3,6)

5912 No (even, but the sum of the digits = 17 which is not divisible by 3 so it is NOT divisible by 6)

507 No (not even, it is not divisible by 2 or 6)

Rule for 9

Any number is divisible 9 if the sum of the number’s digits is divisible by 9.

252 Yes (2+5+2 = 9, 9 is a multiple of 9)

883 No (8+8+3 = 19, not a multiple of 9)

Rule for 10

Any number is divisible by 10, the number ends in 0.

760 Yes Ends in 0

512 No Doesn’t end in 0

Video Tutorial

Here is a quick video on place value.

Interactive Class

For an interactive middle school math class on this material, click here.