Table Of Divisibility Rules
Number Is Divisible By
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If The Number Meets This Condition
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Example
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| 2
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If its last digit is 0, 2, 4, 6, or 8.
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Examples: 12345678 is divisible by 2 because the last digit is 8.
12345678 ÷ 2 = 6172839.
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| 3
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If the sum of its digits are divisible by 3.
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Example: 125172 is divisible by 3 because the sum of the digits is divided by 3.
1 + 2 + 5 + 1 + 7 + 2 = 18.
18 ÷ 3 = 6.
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| 4
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If its last two digits (taken together as a two-digit number) are divisible by 4.
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Example: 1520 is divisible by 4 because the last two digit number pair (20) can
be divided by 4.
1520 ÷ 4 = 380.
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| 5
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If the number ends in 0 or 5.
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Example: 875 is divisible by 5 because the last digit ends in 5.
875 ÷ 5 = 175.
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| 6
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It's even and the sum of its digits are divisible by 3.
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Example: 1232718 is even because the last digit ends in 0, 2, 4, 6, or 8 - 8 in
this case.
Let's do check two; sum the digits and make sure they can be divided by 3.
1 + 2 + 3 + 2 + 7 + 1 + 8 is 24 and 24 ÷ 3 = 8.
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| 7
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This rule applies to three digit numbers only: the quantity "2 x (hundreds digit)
x ten's digit + (last digit)" is divisible by 7.
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Example: 710 is divisible by 7.
((2 × 7) × (1)) + 0 = (14 × 1) + 0 = 14.
14 ÷ 7 = 2.
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| 8
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If the last three digits (taken together as a three-digit number) are divisible
by 8.
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Example: 231912 is divisible by 8.
The last three digits are divisible 912 ÷ 8 = 114.
If this is true, then 231912 ÷ 8 = 28989 must be true.
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| 9
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The sum of its digits is divisible by 9.
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Example: 18726354 is divisible by 9 because the sum of the digits is divisible by
9.
1 + 8 + 7 + 2 + 6 + 3 + 5 + 4 = 36.
36 ÷ 9 = 4.
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| 10
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If the number ends in 0.
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Example: 1234567890 is divisible by 10 because the end digit is 0.
1234567890 ÷ 10 = 123456789.
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