Learn the essential divisibility rules for numbers 2 through 15 with simple examples. Quickly determine if numbers are divisible by 2, 3, 4, 5, and more to solve math problems easily.
1. Divisibility by 2:
If a number ends in 0, 2, 4, 6, or 8, it’s divisible by 2.
Example:
482 ends in 2, so 482 ÷ 2 = 241. It’s divisible by 2.
2. Divisibility by 3:
A number is divisible by 3 if the sum of its digits can be divided by 3 without a remainder.
Example:
For 729, add the digits: 7 + 2 + 9 = 18. Since 18 ÷ 3 = 6, 729 is divisible by 3.
3. Divisibility by 4:
If the last two digits of a number form a number that’s divisible by 4, the whole number is divisible by 4.
Example:
316 has 16 as the last two digits. Since 16 ÷ 4 = 4, 316 is divisible by 4.
4. Divisibility by 5:
Numbers that end in 0 or 5 are always divisible by 5.
Example:
785 ends in 5, so 785 ÷ 5 = 157. It’s divisible by 5.
5. Divisibility by 6:
A number is divisible by 6 if it passes the rules for both 2 and 3.
Example:
132 ends in 2 (so it’s divisible by 2), and the sum of its digits (1 + 3 + 2 = 6) is divisible by 3. Therefore, 132 is divisible by 6: 132 ÷ 6 = 22.
6. Divisibility by 8:
A number is divisible by 8 if the last three digits form a number divisible by 8.
Example:
For 5,128, the last three digits are 128. Since 128 ÷ 8 = 16, 5,128 is divisible by 8.
7. Divisibility by 9:
If the sum of a number’s digits is divisible by 9, the number is too.
Example:
For 4,572, add the digits: 4 + 5 + 7 + 2 = 18. Since 18 ÷ 9 = 2, 4,572 is divisible by 9.
8. Divisibility by 10:
A number is divisible by 10 if it ends in 0.
Example:
470 ends in 0, so 470 ÷ 10 = 47. It’s divisible by 10.
9. Divisibility by 11:
A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is 0 or divisible by 11.
Example:
For 2728, the sum of digits in odd positions (2 + 2 = 4) and the sum in even positions (7 + 8 = 15) have a difference of 11 (15 – 4 = 11). Since 11 is divisible by 11, 2728 is divisible by 11.
10. Divisibility by 15:
A number is divisible by 15 if it’s divisible by 3 and 5.
Example:
225 ends in 5 (so divisible by 5), and the sum of its digits (2 + 2 + 5 = 9) is divisible by 3. Thus, 225 is divisible by 15: 225 ÷ 15 = 15.
