Math
Divisibility Test Calculator
Type a whole number of any size and see every divisibility rule from 2 to 13 applied to it: which digits to look at, the digit sum or alternating sum, and the repeated chop steps for 7 and 13.
Add a custom divisor to check anything else with the quotient and remainder. Big integers are exact, so 40-digit numbers work.
Any whole number (up to 50 digits). Negative signs are ignored for the tests.
Also check divisibility by this number directly.
Try an example
Result
Divisible by (2–13)
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- Not divisible by
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- Custom divisor
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- Digit sum
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
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Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the divisibility test calculator solves
Divisibility rules let you decide whether one number divides another without doing the division. They rely on place value: because 10 is divisible by 2 and 5, only the last digit matters for those; because 10 leaves remainder 1 when divided by 3 or 9, the digit sum decides; because 10 leaves remainder -1 for 11, the alternating sum decides. This calculator applies all twelve rules and shows the arithmetic each one uses.
| Divisor | Rule | Example |
|---|---|---|
| 2 | Last digit is even | 123456 → 6 is even ✓ |
| 3 | Digit sum divisible by 3 | 1+2+3+4+5+6 = 21 ✓ |
| 4 | Last two digits divisible by 4 | 56 ÷ 4 = 14 ✓ |
| 5 | Ends in 0 or 5 | 123456 ends in 6 ✗ |
| 6 | Divisible by 2 and 3 | both ✓ |
| 7 | Chop last digit, double it, subtract | 12345 - 12 = 12333 → 1233 - 6 = 1227 → 122 - 14 = 108 → 108 ÷ 7 ✗ |
| 8 | Last three digits divisible by 8 | 456 ÷ 8 = 57 ✓ |
| 9 | Digit sum divisible by 9 | 21 ✗ |
| 10 | Ends in 0 | ✗ |
| 11 | Alternating sum divisible by 11 | 6-5+4-3+2-1 = 3 ✗ |
| 12 | Divisible by 3 and 4 | both ✓ |
| 13 | Chop last digit, add 4 × it | 12345 + 24 = 12369 → 1236 + 36 = 1272 → 127 + 8 = 135 → 135 ÷ 13 ✗ |
How to use it
- Enter the whole number you want to test.
- Optionally enter a custom divisor for a direct quotient-and-remainder check.
- Read the list of divisors from 2 to 13 that work, then open the steps to see each rule's arithmetic.
How to read the answer
Each step shows the rule, the digits or sums it uses, and the verdict. A number divisible by 6 must pass both the 2 and 3 tests; one divisible by 12 must pass 3 and 4. The custom divisor line uses real division and reports the remainder, so a remainder of 0 means divisible.
Common mistakes and edge cases
- Checking the whole number for 4 or 8 instead of just the last two or three digits.
- Using the plain digit sum for 11; it needs the alternating sum (subtract, add, subtract from the right).
- Combining 2 and 6 to test 12. Use 3 and 4, which share no factor.
- Stopping the 7-rule after one step on a big number; repeat until the number is small enough to recognize.
- Forgetting that 0 is divisible by everything and that negatives divide the same way as their How far a number sits from zero, so the answer is never negative..
Worked examples
123456
Divisible by 2, 3, 4, 6, 8, and 12.
Divisible by (2–13)
2, 3, 4, 6, 8, 12
Divisible by 7 and 13: 1001
1001 = 7 × 11 × 13.
Divisible by (2–13)
7, 11, 13
Prime number 97
Nothing from 2 to 13 divides it.
Divisible by (2–13)
none of 2 through 13
Multiple of everything: 360360
360360 = 2³ × 3² × 5 × 7 × 11 × 13 is divisible by every number from 2 to 13.
Divisible by (2–13)
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Big number
A 25-digit number tested exactly.
Divisible by (2–13)
3, 5
Zero
Divisible by every number.
Divisible by (2–13)
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Decimal input
Whole numbers only.
Divisible by (2–13)
Error
Frequently asked questions
What is the divisibility rule for 7?+
Remove the last digit, double it, and subtract from what is left. Repeat until the number is small. If the result is divisible by 7 (including 0), so was the original: 343 → 34 - 6 = 28 = 7 × 4 ✓.
What is the divisibility rule for 11?+
Alternately subtract and add the digits starting from the right. If the result is 0 or a multiple of 11, the number is divisible by 11: 2728 → 8 - 2 + 7 - 2 = 11 ✓.
How do I test divisibility by 13?+
Remove the last digit, multiply it by 4, and add it to the rest. Repeat. 1001 → 100 + 4 = 104 → 10 + 16 = 26 = 13 × 2 ✓.
Why does the digit sum work for 3 and 9?+
Every power of 10 leaves remainder 1 when divided by 9 (and by 3), so a number and its digit sum leave the same remainder. If the digit sum is divisible by 9, so is the number.
Why do I only look at the last two digits for 4?+
100 is divisible by 4, so everything in the hundreds place and above contributes a multiple of 4. Only the tens and ones digits can spoil it.
Is every number divisible by 1?+
Yes. Dividing by 1 always leaves remainder 0, which is why the rules start at 2.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026