Divisibility Checker
A divisibility rule lets you tell whether one number divides another without doing the division. They are quick mental checks that make factoring and simplifying fractions much faster. This checker tests your number against the common rules and shows the digits it used, so you learn the rule as well as the answer.
How to use the divisibility checker
- Type a whole number, up to 18 digits.
- Read each row: it says Yes or No and shows the digits or sum it checked.
- Try a few numbers and watch how the rule for 3 and 9 both use the digit sum.
Formula
| Divisor | Rule |
|---|---|
| 2 | Last digit is even |
| 3 | Digit sum divisible by 3 |
| 4 | Last two digits divisible by 4 |
| 5 | Ends in 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 8 | Last three digits divisible by 8 |
| 9 | Digit sum divisible by 9 |
| 10 | Ends in 0 |
| 11 | Alternating digit sum divisible by 11 |
Worked examples
123,456
It is even, so it is divisible by 2. The digit sum is 21, which is a multiple of 3 but not of 9, so it is divisible by 3 and 6 but not 9.
A test for 11
918,082: the alternating sum of its digits is 2 − 8 + 0 − 8 + 1 − 9 = −22, a multiple of 11, so the number is divisible by 11.
Why the rules work
Each rule comes from how place value interacts with the divisor.
Rules based on the last digits
Since 10, 100 and 1,000 are all multiples of 2 and 5, only the last digit matters for those. For 4, only the last two digits matter because 100 is a multiple of 4. For 8, the last three matter because 1,000 is a multiple of 8.
Rules based on the digit sum
10 leaves a remainder of 1 when divided by 3 or by 9, and so do 100, 1,000 and so on. So a number has the same remainder as its digit sum, which is why the sum decides divisibility by 3 and 9.
The rule for 11
10 leaves a remainder of −1 when divided by 11, so digits contribute alternately +1 and −1. That is why you alternate the signs.
Combining rules
A number divisible by 2 and 3 is divisible by 6. One divisible by 3 and 4 is divisible by 12. Combine rules only when the divisors share no factors.
Practice problems
Try these yourself first, then check your answer. The answers come from the calculator above.
- Is 20,736 divisible by 3, 4 and 9?
Show answer
Divisible by 2: Yes: last digit is 6
- Is 5,148 divisible by 11?
Show answer
Divisible by 2: Yes: last digit is 8
Common mistakes to avoid
- Using the digit-sum rule for 4 or 8. Those depend on the last digits, not the sum.
- Forgetting that 6 needs both the 2 and the 3 rules.
- Adding digits incorrectly for the rule of 11. You alternate signs.
Frequently asked questions
Why does the digit-sum rule work for 3 and 9?
Because 10 leaves a remainder of 1 when divided by 3 or 9, each digit contributes its own value to the remainder.
Is there a rule for 7?
Yes, but it is clumsy: double the last digit, subtract from the rest and repeat. Division is often quicker.
How are these rules used?
To find factors quickly, simplify fractions and test for primes. See how to simplify fractions.
Does zero count as divisible?
Yes. Zero is divisible by every non-zero number.
Reviewed September 26, 2026 by the SolveCalcPro editorial team. Found a mistake? Tell us; see our editorial policy.