# Divisibility Rules

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Divisibility rules help us work out whether a number is exactly divisible by other numbers (i.e. there is no remainder).

The rules are shortcuts for finding out whether numbers are exactly divisible without doing division calculations. Some of these rules along with examples are illustrated below:

## Divisible by 2?

 Rule: If it ends with a 0, 2, 4, 6, or 8 Number Divisible? Why? 456 Yes The last digit is 6 68 Yes The last digit is 8 25 No The last digit is 5 (not a 2,4,6,or 8) 207 No The last digit is 7 (not a 2,4,6,or 8)

## Divisible by 3?

 Rule: If the sum of the digits is a multiple of 3 Number Divisible? Why? 405 Yes 4 + 0 + 5 = 9 (9 is a multiple of 3) 381 Yes 3 + 8 + 1 = 12 (12 is a multiple of 3) 928 No 9 + 2 + 8 = 19 (19 is not a multiple of 3) 4,616 No 4 + 6 + 1 + 6 = 17 (17 is not a multiple of 3)

 Helper: The multiples of 3 include... 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45

## Divisible by 4?

 Rule: If the last two digits are a multiple of 4 (or if the last two digits are 00) Number Divisible? Why? 348 Yes 48 is a multiple of 4 27,616 Yes 16 is a multiple of 4 8,514 No 14 is not a multiple of 4 722 No 22 is not a multiple of 4 1,200 Yes The last two digits are 00200 is a multiple of 4
 Helper: The multiples of 4 include... 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60

## Divisible by 5?

 Rule: If it ends with a 5 or a 0 Number Divisible? Why? 3,425 Yes The last digit is 5 750 Yes The last digit is 0 8,551 No The last digit is 1 (not a 0 or a 5) 394 No The last digit is 4 (not a 0 or a 5)

## Divisible by 6?

 Rule: If it is divisible by 2 and by 3 Number Divisible? Why? 5,106 Yes The last digit is a 2 (it is a multiple of 2 ) and... 5 + 1 + 0 + 6 = 12 (12 is a multiple of 3) 636 Yes The last digit is a 6 (it is a multiple of 2 ) and... 6 + 3 + 6 = 15 (15 is a multiple of 3) 5,912 No The last digit is a 2 (it is a multiple of 2 ) but... 5 + 9 + 1 + 2 = 17 (17 is not a multiple of 3) 508 No The last digit is a 8 (it is a multiple of 2 ) but... 5 + 0 + 8 = 13 (13 is not a multiple of 3)

## Divisible by 9?

 Rule: If the sum of the digits are a multiple of 9 Number Divisible? Why? 7,686 Yes 7 + 6 + 8 + 6 = 27 (27 is a multiple of 9) 252 Yes 2 + 5 + 2 = 9 (9 is a multiple of 9) 883 No 8 + 8 + 3 = 19 (19 is not a multiple of 9) 5,105 No 5 + 1 + 0 + 5 = 11 (11 is not a multiple of 9)
 Helper: The multiples of 9 include... 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135

## Divisible by 10?

 Rule: If the last digit is 0 Number Divisible? Why? 880 Yes The last digit is 0 9,560 Yes The last digit is 0 312 No The last digit is 2 (not a 0) 7,897 No The last digit is 7 (not a 0)

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