Divisibility Rules

6 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team

A divisibility rule tells you whether one number divides another without carrying out the division. Once you know them, you can factor numbers and simplify fractions in seconds. Here are the rules, why they work and a full worked example.

The rules

Divisor	Rule
2	Last digit is 0, 2, 4, 6 or 8
3	The digits add to a multiple of 3
4	The last two digits form a multiple of 4
5	Ends in 0 or 5
6	Divisible by both 2 and 3
7	Double the last digit and subtract from the rest; the result is a multiple of 7
8	The last three digits form a multiple of 8
9	The digits add to a multiple of 9
10	Ends in 0
11	The alternating sum of digits is a multiple of 11

A worked example: 3,465

Is 3,465 divisible by 3, 5, 9 and 11? Digit sum 3 + 4 + 6 + 5 = 18, a multiple of 3 and 9, so yes to both. It ends in 5, so yes to 5. Alternating sum from the right: 5 − 6 + 4 − 3 = 0, a multiple of 11, so yes. Indeed 3,465 = 3² × 5 × 7 × 11.

The rule for 7

Test 343: double the last digit (3 × 2 = 6) and subtract from the rest: 34 − 6 = 28, which is a multiple of 7, so 343 is divisible by 7 (343 = 7³). If the result is large, repeat the process.

Why the digit-sum rule works

Because 10, 100, 1000… all leave a remainder of 1 when divided by 9 (and by 3), a number has the same remainder as its digit sum. That is why the sum decides divisibility by 3 and 9. Check any number in the divisibility checker.

Putting rules to work

To factor 4,620: it ends in 0 (divisible by 2, 5, 10), digit sum 12 (divisible by 3), last two digits 20 (divisible by 4). Dividing out these factors leads to 4,620 = 2² × 3 × 5 × 7 × 11. To simplify 84/126, the digit sums (12 and 9) show both are divisible by 3, and both are even, so divide by 6, and so on. See simplifying fractions.

Practice questions

Test yourself, then tap to check. Answers are calculated by the tools linked below.

Is 20,736 divisible by 3, 4 and 9?
Show answer
Divisible by 2: Yes: last digit is 6
Factor 252 into primes.
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Prime factorization: 2^2 × 3^2 × 7
List the factors of 48.
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Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48