Prime Numbers — Free KS3 Worksheet
A free, printable KS3 worksheet on prime numbers, with a full worked answer key. 15 questions graded easy to hard for Years 7, 8 and 9, building from spotting small primes up to working out how far you actually have to test.
A prime number has exactly two factors, itself and 1. That word exactly is doing all the work. It is why 1 is not prime, since it has only one factor, and it is why 2 is prime despite being even. Fifteen questions here, and every one of them comes back to counting factors rather than to a memorised list.
What is on the sheet
Small numbers first, deciding prime or not by finding the factors. Then picking primes out of a mixed set, including 2, which trips people up more than any other number on the sheet. The middle questions use a sieve up to 30, where crossing out multiples shows what is left. The last three are a stretch on the stopping rule: you only need to test divisors up to the square root, so 97 takes four checks rather than ninety-five. The final question puts that bound to work on 143, which looks prime and is not.
Marking it
If 143 came out as prime, the stopping rule has been applied but the divisor 11 was skipped. The prime numbers lesson works that exact question through.
Keep going
More number properties practice
Factors and Multiples — Free KS3 Worksheet
A free, printable KS3 worksheet on factors and multiples, with a full worked answer key. 15 questions graded easy to hard for Years 7, 8 and 9, building from listing factors and multiples up to knowing exactly where to stop.
Square and Cube Roots — Free KS3 Worksheet
A free, printable KS3 worksheet on square and cube roots, with a full worked answer key. 15 questions graded easy to hard for Years 7, 8 and 9, building from square roots and cube roots up to estimating a root that isn't exact, and worded garden and box problems.
Square and Cube Numbers — Free KS3 Worksheet
A free, printable KS3 worksheet on square and cube numbers, with a full worked answer key. 16 questions graded easy to hard for Years 7, 8 and 9, building from squares and cubes up to higher powers, mixed calculations and worded patio and box problems.
Want all 8 number properties worksheets at once?
One PDF, 125 questions, every answer key included, in teaching order. Every sheet in it is free on its own page too. The pack just saves you collecting them one at a time.