Practice Prime numbers and prime factorisation
A prime number is a whole number greater than one with exactly two positive divisors: one and itself.
Prime factors help you simplify fractions and understand number structure.
Exercises with solutions
A prime number is a natural number greater than 1 that is divisible only by 1 and itself. To check whether a number is prime, test divisibility by all primes up to the square root of the number. If none divides it, the number is prime.
Exercise 1
Is 1 a prime number?
Show solution and working
No
A prime number must be greater than 1. The number 1 has only a single divisor and therefore does not count.
Exercise 2
List all prime numbers up to 20.
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2, 3, 5, 7, 11, 13, 17, 19
2 is the only even prime. 9 = 3 · 3, 15 = 3 · 5 and 20 = 4 · 5 are not prime.
Exercise 3
Is 91 a prime number?
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No, because 91 = 7 · 13
The square root of 91 is about 9.5, so you only need to test the primes 2, 3, 5 and 7. 91 ÷ 7 = 13 leaves no remainder.
Exercise 4
Write 60 as a product of primes.
Show solution and working
60 = 2 · 2 · 3 · 5
60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5, and 5 is prime. Check: 2 · 2 · 3 · 5 = 60.
Common mistake
Treating 1 as a prime number. Also, one divisor is enough as a counterexample: whoever finds 91 = 7 · 13 does not need to test further.
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