Which numbers make a rectangle?
Twenty-four squares. Four across and they sit in a neat block; five across and one is left over on its own. Pull the block wider and narrower to find the widths that come out even. Those are the factors, and some numbers have hardly any.
24 = 4 × 6
- This number is
- composite
- Its factors
- 1, 2, 3, 4, 6, 8, 12, 24
How many squares
1 to 36 — past that the narrow widths are too many rows to see.
Drag the right-hand edge of the block, or click one of the widths underneath it.
Ready to try some? Factors and multiples worksheets
Where it usually goes wrong
Factors get hunted for by feel, so 15 gets called prime for being odd and awkward, and 1 and the number itself get left off the list. A factor is a width that fills the block with no gap left over — which is a thing to look at rather than a thing to remember.
Try this
- Set it to 24 and pull the block through every width. Eight of them come out even; the rest leave a square stranded.
- Now try 13. Only the single line works, and that is what a prime number looks like.
- Try 25 and then 36. Square numbers make an actual square, and it is the only shape whose two sides are the same.
Where this goes next
Prime factorization, common denominators and canceling fractions all start with being able to see what a number is made of.