Divisibility Rules

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

NumberDivisible?Why?
456YesThe last digit is 6
68YesThe last digit is 8
25NoThe last digit is 5 (not a 2,4,6,or 8)
207NoThe last digit is 7 (not a 2,4,6,or 8)

Back To All Divisibility Rules

Divisible by 3?

Rule: If the sum of the digits is a multiple of 3

NumberDivisible?Why?
405Yes4 + 0 + 5 = 9 (9 is a multiple of 3)
381Yes3 + 8 + 1 = 12 (12 is a multiple of 3)
928No9 + 2 + 8 = 19 (19 is not a multiple of 3)
4,616No4 + 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

Back To All Divisibility Rules

Divisible by 4?

Rule: If the last two digits are a multiple of 4
(or if the last two digits are 00)

NumberDivisible?Why?
348Yes48 is a multiple of 4
27,616Yes16 is a multiple of 4
8,514No14 is not a multiple of 4
722No22 is not a multiple of 4
1,200YesThe 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

Back To All Divisibility Rules

Divisible by 5?

Rule: If it ends with a 5 or a 0

NumberDivisible?Why?
3,425YesThe last digit is 5
750YesThe last digit is 0
8,551NoThe last digit is 1 (not a 0 or a 5)
394NoThe last digit is 4 (not a 0 or a 5)

Back To All Divisibility Rules

Divisible by 6?

Rule: If it is divisible by 2 and by 3

NumberDivisible?Why?
5,106YesThe last digit is a 2 (it is a multiple of 2 ) and…5 + 1 + 0 + 6 = 12 (12 is a multiple of 3)
636YesThe last digit is a 6 (it is a multiple of 2 ) and…6 + 3 + 6 = 15 (15 is a multiple of 3)
5,912NoThe last digit is a 2 (it is a multiple of 2 ) but…5 + 9 + 1 + 2 = 17 (17 is not a multiple of 3)
508NoThe last digit is a 8 (it is a multiple of 2 ) but…5 + 0 + 8 = 13 (13 is not a multiple of 3)

Back To All Divisibility Rules

Divisible by 9?

Rule: If the sum of the digits are a multiple of 9

NumberDivisible?Why?
7,686Yes7 + 6 + 8 + 6 = 27 (27 is a multiple of 9)
252Yes2 + 5 + 2 = 9 (9 is a multiple of 9)
883No8 + 8 + 3 = 19 (19 is not a multiple of 9)
5,105No5 + 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

Back To All Divisibility Rules

Divisible by 10?

Rule: If the last digit is 0

NumberDivisible?Why?
880YesThe last digit is 0
9,560YesThe last digit is 0
312NoThe last digit is 2 (not a 0)
7,897NoThe last digit is 7 (not a 0)

Back To All Divisibility Rules