Divisibility by 2
Rule: Check the last digit. If it's 0, 2, 4, 6, or 8, the number is divisible by 2.
723 → last digit 3 → not divisible by 2 ✗
Divisibility by 3
Rule: Add up every digit. If that total divides evenly by 3, so does the original number.
217 → 2+1+7 = 10, 10÷3 ≠ whole → not divisible by 3 ✗
Divisibility by 4
Rule: Look only at the last two digits as their own two-digit number. If that divides by 4, the whole number does too.
1,034 → last two digits: 34 → 34÷4 = 8.5 → not divisible by 4 ✗
Divisibility by 5
Rule: A number divides by 5 only when it ends in 0 or 5.
1,746 → last digit 6 → not divisible by 5 ✗
Divisibility by 6
Rule: It has to pass both the 2 test and the 3 test at once: even, with a digit sum that divides by 3.
254 → even ✓, 2+5+4=11 (not ÷3) ✗ → not divisible by 6
Divisibility by 7
Rule: Chop off the last digit, double it, and subtract that from what's left. If the result divides by 7, so does the original. (Repeat on bigger numbers if needed.)
205: last digit 5 × 2 = 10, 20 − 10 = 10, not ÷7 → not divisible by 7 ✗
Divisibility by 8
Rule: Take the last three digits as their own number. If that divides by 8, the whole thing does too.
1,234 → 234÷8 = 29.25 → not divisible by 8 ✗
Divisibility by 9
Rule: Same idea as the 3 test, just stricter - add all the digits and check whether that sum divides by 9.
456 → 4+5+6 = 15, 15÷9 ≠ whole → not divisible by 9 ✗
Divisibility by 10
Rule: The simplest one on this list - the number just has to end in 0.
Divisibility by 11
Rule: Starting from the right, alternately add and subtract each digit. Land on 0 or a multiple of 11 and the original number passes too.
2,728 → 2−7+2−8 = −11 → divisible by 11 ✓
1,234 → 1−2+3−4 = −2 → not divisible by 11 ✗
Quick Reference
| Divisible by | Rule |
|---|---|
| 2 | Last digit is even |
| 3 | Digits add up to a multiple of 3 |
| 4 | Last two digits divide by 4 |
| 5 | Ends in 0 or 5 |
| 6 | Passes both the 2 and 3 tests |
| 7 | Double last digit, subtract from the rest |
| 8 | Last three digits divide by 8 |
| 9 | Digits add up to a multiple of 9 |
| 10 | Ends in 0 |
| 11 | Alternating digit sum divides by 11 |