Have you ever watched a student stare at a fraction like 144/216 wondering what number can divide both the top and bottom? Divisibility rules are like cheat codes for arithmetic. They let you determine if a number divides evenly without doing any long division.
1. Divisible by 2
The number ends in an even digit: 0, 2, 4, 6, or 8.
Example: 1,498 ends in 8, so it is divisible by 2.
2. Divisible by 3
Add up all the digits. If the sum is divisible by 3, the whole number is divisible by 3.
Example: Is 456 divisible by 3? Add 4 + 5 + 6 = 15. Since 15 is divisible by 3, 456 is too!
3. Divisible by 4
Look only at the last two digits. If the last two digits form a number divisible by 4, the whole number is.
Example: 5,724. Look at 24. Since 24 ÷ 4 = 6, 5,724 is divisible by 4.
4. Divisible by 5
The number ends in either 0 or 5.
Example: 3,495 ends in 5, so it is divisible by 5.
5. Divisible by 6
The number must pass BOTH the rule for 2 (even) AND the rule for 3 (digit sum divisible by 3).
Example: 732. It is even (ends in 2). Sum of digits: 7 + 3 + 2 = 12 (divisible by 3). Therefore, 732 is divisible by 6!
6. Divisible by 9
Add all the digits together. If the sum is divisible by 9, the number is divisible by 9.
Example: 2,853. Add 2 + 8 + 5 + 3 = 18. Since 18 is divisible by 9, 2,853 is divisible by 9!