Module 3 · Factors and multiples · Lesson 7 of 39
Divisibility and divisibility rules
Tell whether one number divides another without doing the division.
In this lesson · about 14 minutes
- Explain what it means for one whole number to be divisible by another
- Use the divisibility rules for 2, 3, 4, 5, 6, 8, 9 and 10
15 is divisible by 5 because 15 ÷ 5 = 3, a whole number. In other words, 15 can be cut into equal pieces of size 5 with nothing left over: the remainder is 0.
9 is not divisible by 4. 4 goes into 9 two times (that's 8), with a remainder of 1. Because there's a remainder, the answer isn't a whole number.
Divisibility rules
These shortcuts tell you the answer without dividing.
| Divisible by | If… | Example |
|---|---|---|
| 2 | the last digit is 0, 2, 4, 6 or 8 | 24: last digit 4 |
| 3 | the sum of the digits is divisible by 3 | 123: 1 + 2 + 3 = 6 |
| 4 | the last two digits are divisible by 4 | 3,448: 48 ÷ 4 = 12 |
| 5 | the last digit is 0 or 5 | 2,360 |
| 6 | it is divisible by both 2 and 3 | 330: even, and 3 + 3 + 0 = 6 |
| 7 | 5 × last digit + the rest is divisible by 7 (or: rest − 2 × last digit) | 256: 25 + 30 = 55, not divisible, so 256 isn't |
| 8 | the last three digits are divisible by 8 | 34,256: 256 ÷ 8 = 32 |
| 9 | the sum of the digits is divisible by 9 | 3,254: digit sum 14, so no |
| 10 | the last digit is 0 | 125: last digit 5, so no |
Worked example
Is 56 divisible by 8?
Use the definition: do the division and see whether the result is a whole number.
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