Prime or compositeNumbers to 50
Name: Date:
Circle whether each number is prime or composite.
144PrimeComposite
210PrimeComposite
339PrimeComposite
425PrimeComposite
523PrimeComposite
619PrimeComposite
746PrimeComposite
821PrimeComposite
Prime or composite worksheets
A prime number has exactly two factors: one and itself. Everything else above one is composite. These free printable worksheets give a number and ask which it is, with an answer key that shows the factor that settles each composite.
If they get stuck
Prime or composite
The answer key prints on a separate page.
What's on this sheet
The sheets are built to defeat the shortcut, which is the only interesting thing about designing them. Every prime except 2 is odd, so a page whose composites are all even numbers can be answered at speed by a child who has learned nothing: call the evens composite, call the odds prime, score nearly full marks. So the odd composites are drawn as their own group and every page contains some — 9, 15, 21, 25, 33, 35, 49 are the numbers that make this a real question, and a sheet without them is testing odd and even while calling it primality.
Why this sheet works
The band is the difficulty, and it is not just about bigger numbers. Up to 30, a composite gives itself away to the 2, 3 and 5 times tables. Past 50 the sheet starts asking about 91 and 97, where the only honest method is dividing by each prime up to the square root — and testing every candidate up to 100 is exactly the range the standard names.
How this one works
Is 44 prime?
44
√44≈6
tried:2
44 ÷ 2 =22
- A prime has exactly two factors: 1 and itself. So the question is whether anything ELSE divides into 44.
- You do not have to try everything up to 44. Factors come in pairs, so if one were bigger than 6 its partner would be smaller — and you would have found that one first. Testing up to 6 is enough.
- 2 goes into 44 exactly (44 ÷ 2 = 22), and that is one factor too many. 44 is composite — no need to test any further.