| ÷ By | Divisibility Test | Example |
| 2 | if the last digit is 0, 2, 4, 6 or 8 | 168 is divisible by 2, the last digit is 8 |
| 3 | if the sum of the digits is divisible by 3 | 168 is divisible by 3, the sum of the digits is 15 (1+6+8=15), and 15 is divisible by 3 |
| 4 | if the the last two digits are divisible by 4 | 316 is divisible by 4, 16 is divisible by 4 |
| 5 | if the last digit is either 0 or 5 | 195 is divisible by 5, the last digit is 5 |
| If you have a test for divisibility for any two numbers m and n, and m and n have no factors in common, then you can combine the tests to create a test for m × n. For an example of this, see 12. Try to think of tests for divisibility by 14, 15, 18, and 20 | ||
| 6 | if it is divisible by 2 & it is divisible by 3 | 168 is divisible by 6, it is by 2 & 3 |
| "Repeat the procedure so the numbers N > N' > N'' >...> N* are created. Check the rule for divisibility." | ||
| 7 | "Double the units and subtract from the tens", e.g. 1365 ->136-(2x5)=126 ->12-(2x6)=0. If the chain ends in zero or a multiple of 7, then the original number is divisible by 7" | |
| 8 | if the last three digits are divisible by 8 | 7,120 is divisible by 8. 120 is by 8 |
| 9 | if the sum of the digits is divisible by 9 | 549 is divisible by 9, the sum of the digits is 18 (5+4+9=18), and 18 is divisible by 9 |
| 10 | if the last digit is 0 | 1,470 is divisible by 10, the last digit is 0 |
| 11 | "Subtract the units from the tens", e.g. 1364 -> 136-4 etc. If the chain ends in zero, then the original number is divisible by 11" |
34871903
→ 3487190 - 3 = 3487187 3487187 → 348718 - 7 = 348711 348711 → 34871 - 1 = 34870 the end |
| 12 | if it is divisible by 4 and divisible by 3 | 724560 is divisible by 12, the number formed by its last two digits, 60, is divisible by 4, and the sum of its digits is 30, which is divisible by 3 |
| 13 | "Add the tens to 4 times the units", e.g. 1365 -> 136+20 etc. If the chain ends in a multiple of 13, then the original number is divisible by 13" | |
| 14 | if it is divisible by 7 and divisible by 2 | |
| 15 | if it is divisible by 3 and divisible by 5 | |
| 16 | if the last four digits are divisible by 16 | |
| 17 | "Two times the hundreds less the last two digits, e.g. 8517 -> 2*85 -17, etc...." If the chain ends in a multiple of 17, then the original number is divisible by 17" | |
| 18 | if it is divisible by 2 and divisible by 9 | |
| 19 | "Add the hundreds to 4 times the rest", e.g. 1311 -> 13+44 etc. If the chain ends in a multiple of 19, then the original number is divisible by 19" | |
| 20 | if its units digit is 0, and its tens digit is even | |