Finding factor pairs with arrays
An array is a rectangle of objects arranged in equal rows. A 3 × 5 array has 3 rows of 5, which is 15 objects. Every array you can make with a number of blocks gives you a factor pair of that number.
The pair-up method
To list all the factors of 48, start at 1 and work upwards. Write each pair as you find it, and stop when the numbers meet.
| Try | Divides 48? | Pair |
|---|---|---|
| 1 | yes | 1 × 48 |
| 2 | yes | 2 × 24 |
| 3 | yes | 3 × 16 |
| 4 | yes | 4 × 12 |
| 5 | no | - |
| 6 | yes | 6 × 8 |
| 7 | no | - (7 × 7 is 49, so we can stop) |
So the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. That is ten factors in five pairs.
Why squares are special
For 36 the pairs are 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6. The last pair uses the same number twice, so it only adds one new factor. Square numbers are the only numbers with an odd count of factors: 36 has nine.
Turn arrays around
A 4 × 12 array turned on its side is a 12 × 4 array. The total does not change. That is the commutative property, and it is the reason children only need to learn about half of the times-table facts.
Type 48 into the Number Blocks Tool and compare its rectangles with the table above. Open the tool with 48
List the factor pairs
Write every factor pair for each number, starting from 1.
- 18
- 25
- 30
Show answers
- 1 × 18, 2 × 9, 3 × 6.
- 1 × 25, 5 × 5 (three factors, because 25 is square).
- 1 × 30, 2 × 15, 3 × 10, 5 × 6.