What are divisibility rules?
Divisibility rules are shortcuts that help you quickly tell if one number can be divided evenly by another, without having to actually do the division.
- To check if 24 is divisible by 2, look at the last digit. Since it is even (4), 24 ÷ 2 = 12 with no remainder.
“Divisible” means the number divides evenly with no remainder.
Divisibility rule for 2
A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
- 36 → last digit is 6, so 36 ÷ 2 = 18 (divisible)
- 57 → last digit is 7, not even, so not divisible by 2
Even numbers are always divisible by 2.
Divisibility rule for 3
A number is divisible by 3 if the sum of its digits is divisible by 3.
- 123 → 1 + 2 + 3 = 6, which is divisible by 3 → 123 ÷ 3 = 41
- 124 → 1 + 2 + 4 = 7, not divisible by 3 → not divisible
If you get a large sum, you can repeat the rule until the sum is small enough.
Divisibility rule for 4
A number is divisible by 4 if the last two digits form a number divisible by 4.
- 316 → last two digits 16, divisible by 4 → 316 ÷ 4 = 79
- 318 → last two digits 18, not divisible by 4 → not divisible
Only the last two digits matter for this rule.
Divisibility rule for 5
A number is divisible by 5 if its last digit is 0 or 5.
- 85 → ends in 5 → divisible by 5
- 82 → ends in 2 → not divisible by 5
Numbers ending in 0 or 5 are multiples of 5.
Divisibility rule for 6
A number is divisible by 6 if it is divisible by both 2 and 3.
- 132 → even (divisible by 2) and digit sum is 6 (divisible by 3) → divisible by 6
- 135 → digit sum is 9 (divisible by 3), but not even → not divisible by 6
You must check both rules: 2 and 3.
Divisibility rule for 8
A number is divisible by 8 if the last three digits form a number divisible by 8.
- 2,416 → last three digits 416 → divisible by 8 → 2,416 ÷ 8 = 302
- 2,414 → last three digits 414 → not divisible by 8 → not divisible
For small numbers, you can just check directly. For larger numbers, use the last three digits rule.
Divisibility rule for 9
A number is divisible by 9 if the sum of its digits is divisible by 9.
- 729 → 7 + 2 + 9 = 18, divisible by 9 → 729 ÷ 9 = 81
- 731 → 7 + 3 + 1 = 11, not divisible by 9 → not divisible
This rule is similar to the divisibility rule for 3, but only works when the sum is a multiple of 9.
Divisibility rule for 10
A number is divisible by 10 if its last digit is 0.
- 120 → ends in 0 → divisible by 10
- 125 → ends in 5 → not divisible by 10
All multiples of 10 end with a 0.