Divisibility Rules

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

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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)

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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

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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 00
200 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

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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)

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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)

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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

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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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