Divisibility Rules (1 to 20) Quick Reference
Divisibility rules let you test whether a number divides evenly without long division. This quick reference gives the rule and a worked example for every divisor from 1 to 20, plus a live checker.
By 2Last digit even0, 2, 4, 6 or 8
By 3Digit sum ÷ 34521: 4 + 5 + 2 + 1 = 12
By 5Ends in 0 or 58745 ends in 5
By 9Digit sum ÷ 96372: 6 + 3 + 7 + 2 = 18
By 10Ends in 04560 ends in 0
By 11Alternating digit sum8272: 8 − 2 + 7 − 2 = 11
Divisibility Checker
Tip: open this page with ?divisor=7 (any divisor from 1 to 20) to start with that divisor, a matching example number, and its row highlighted.
| Divisor | Divisibility Rule Condition | Step-by-Step Example | Copy Rule |
|---|---|---|---|
| 1 | Every whole number is divisible by 1. | Is 2025 divisible by 1? Every whole number is divisible by 1. So 2025 is divisible by 1. | |
| 2 | The last digit is 0, 2, 4, 6 or 8. | Is 3846 divisible by 2? Last digit is 6, which is even. So 3846 is divisible by 2. | |
| 3 | The sum of the digits is divisible by 3. | Is 4521 divisible by 3? Digit sum: 4 + 5 + 2 + 1 = 12. 12 is divisible by 3. So 4521 is divisible by 3. | |
| 4 | The last two digits form a number divisible by 4. | Is 7316 divisible by 4? Last two digits: 16. 16 is divisible by 4. So 7316 is divisible by 4. | |
| 5 | The last digit is 0 or 5. | Is 8745 divisible by 5? Last digit is 5, which is 0 or 5. So 8745 is divisible by 5. | |
| 6 | The number is divisible by both 2 and 3. | Is 2418 divisible by 6? Test 2: last digit 8 (yes). Test 3: digit sum 15 (yes). Both pass. So 2418 is divisible by 6. | |
| 7 | Double the last digit and subtract it from the rest of the number. Repeat until the result is small. If it is divisible by 7 (0 counts), so is the number. | Is 2149 divisible by 7? 214 − 2×9 = 196; 19 − 2×6 = 7. 7 is divisible by 7. So 2149 is divisible by 7. | |
| 8 | The last three digits form a number divisible by 8. | Is 7128 divisible by 8? Last three digits: 128. 128 is divisible by 8. So 7128 is divisible by 8. | |
| 9 | The sum of the digits is divisible by 9. | Is 6372 divisible by 9? Digit sum: 6 + 3 + 7 + 2 = 18. 18 is divisible by 9. So 6372 is divisible by 9. | |
| 10 | The last digit is 0. | Is 4560 divisible by 10? Last digit is 0, which is 0. So 4560 is divisible by 10. | |
| 11 | Add and subtract the digits alternately (+, −, +, −, ...). If the result is divisible by 11 (0 counts), so is the number. | Is 8272 divisible by 11? Alternating digit sum: 8 − 2 + 7 − 2 = 11. 11 is divisible by 11. So 8272 is divisible by 11. | |
| 12 | The number is divisible by both 3 and 4. | Is 5244 divisible by 12? Test 3: digit sum 15 (yes). Test 4: last two digits 44 (yes). Both pass. So 5244 is divisible by 12. | |
| 13 | Multiply the last digit by 4 and add it to the rest of the number. Repeat until the result is small. If it is divisible by 13, so is the number. | Is 3159 divisible by 13? 315 + 4×9 = 351; 35 + 4×1 = 39. 39 is divisible by 13. So 3159 is divisible by 13. | |
| 14 | The number is divisible by both 2 and 7. | Is 2086 divisible by 14? Test 2: last digit 6 (yes). Test 7: reduced value 7 (yes). Both pass. So 2086 is divisible by 14. | |
| 15 | The number is divisible by both 3 and 5. | Is 4215 divisible by 15? Test 3: digit sum 12 (yes). Test 5: last digit 5 (yes). Both pass. So 4215 is divisible by 15. | |
| 16 | The last four digits form a number divisible by 16. | Is 90144 divisible by 16? Last four digits: 144. 144 is divisible by 16. So 90144 is divisible by 16. | |
| 17 | Multiply the last digit by 5 and subtract it from the rest of the number. Repeat until the result is small. If it is divisible by 17, so is the number. | Is 2975 divisible by 17? 297 − 5×5 = 272; 27 − 5×2 = 17. 17 is divisible by 17. So 2975 is divisible by 17. | |
| 18 | The number is divisible by both 2 and 9. | Is 3942 divisible by 18? Test 2: last digit 2 (yes). Test 9: digit sum 18 (yes). Both pass. So 3942 is divisible by 18. | |
| 19 | Multiply the last digit by 2 and add it to the rest of the number. Repeat until the result is small. If it is divisible by 19, so is the number. | Is 1653 divisible by 19? 165 + 2×3 = 171; 17 + 2×1 = 19. 19 is divisible by 19. So 1653 is divisible by 19. | |
| 20 | The last two digits form a number divisible by 20 (00, 20, 40, 60 or 80). | Is 7840 divisible by 20? Last two digits: 40. 40 is divisible by 20. So 7840 is divisible by 20. |
| Divisor | Factors to Test | Condition | Example | Copy |
|---|---|---|---|---|
| 6 | 2 × 3 = 6 | Divisible by both 2 and 3 | 2418 is divisible by 2 and by 3, so by 6 | |
| 10 | 2 × 5 = 10 | Divisible by both 2 and 5 | 4560 is divisible by 2 and by 5, so by 10 | |
| 12 | 3 × 4 = 12 | Divisible by both 3 and 4 | 5244 is divisible by 3 and by 4, so by 12 | |
| 14 | 2 × 7 = 14 | Divisible by both 2 and 7 | 2086 is divisible by 2 and by 7, so by 14 | |
| 15 | 3 × 5 = 15 | Divisible by both 3 and 5 | 4215 is divisible by 3 and by 5, so by 15 | |
| 18 | 2 × 9 = 18 | Divisible by both 2 and 9 | 3942 is divisible by 2 and by 9, so by 18 | |
| 20 | 4 × 5 = 20 | Divisible by both 4 and 5 | 7840 is divisible by 4 and by 5, so by 20 | |
| 8 | 2 × 4 ≠ 8 | Do NOT combine 2 and 4: they share the factor 2 | 12 is divisible by 2 and by 4, but not by 8. Use the last three digits instead |
| Prime | Quick Test | Example Number | Prime Factorization | Copy |
|---|---|---|---|---|
| 2 | Last digit is even | 1200 | 24 × 3 × 52 | |
| 3 | Digit sum divisible by 3 | 1053 | 34 × 13 | |
| 5 | Last digit is 0 or 5 | 2625 | 3 × 53 × 7 | |
| 7 | Double last digit, subtract | 2149 | 7 × 307 | |
| 11 | Alternating digit sum | 8272 | 24 × 11 × 47 | |
| 13 | Last digit × 4, add | 3159 | 35 × 13 | |
| 17 | Last digit × 5, subtract | 2975 | 52 × 7 × 17 | |
| 19 | Last digit × 2, add | 1653 | 3 × 19 × 29 |
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Frequently Asked Questions
| Question | Answer |
|---|---|
| What are divisibility rules? | Divisibility rules are shortcuts that tell you whether a number divides evenly by another number without doing long division, for example by looking at the last digit or adding the digits. |
| How do you check if a number is divisible by 7? | Double the last digit and subtract it from the rest of the number, and repeat. For 2149: 214 − 2 × 9 = 196, then 19 − 2 × 6 = 7, which is divisible by 7, so 2149 = 7 × 307. |
| What is the divisibility rule for 11? | Add and subtract the digits alternately. If the result is 0 or a multiple of 11, the number is divisible by 11. For 8272: 8 − 2 + 7 − 2 = 11, so 8272 is divisible by 11. |
| How do you test divisibility by 6, 12, 15 and 18? | Test two coprime factors together: 6 is 2 and 3, 12 is 3 and 4, 15 is 3 and 5, and 18 is 2 and 9. If a number passes both tests it is divisible by the product. |
| Why is it not enough to test 2 and 4 for divisibility by 8? | 2 and 4 share the factor 2. The number 12 is divisible by both 2 and 4 but not by 8. For 8 you must check that the last three digits form a number divisible by 8. |
| How are divisibility rules used in prime factorization? | You test the small primes 2, 3, 5, 7, 11, 13, 17 and 19 in order and divide out each one that passes. For 1716: 1716 = 2 × 2 × 3 × 11 × 13, so 1716 = 22 × 3 × 11 × 13. |