Prime Numbers and Prime Factorisation

A prime number is a whole number with exactly two different factors: 1 and itself. So 2 is prime, because only 1 and 2 divide into it, but 4 is not, because 1, 2 and 4 all do. The primes below 20 are 2, 3, 5, 7, 11, 13, 17 and 19. Every whole number above 1 is made by multiplying primes.

No. A prime number must have exactly two different factors, 1 and itself, and 1 has only one factor: itself. So 1 is not prime, and 2, not 1, is the smallest prime number. Zero is not prime either.

Yes. The only factors of 2 are 1 and 2, so it has exactly two factors and is prime; it is also the smallest prime number. It is the only even prime, because every other even number has 2 as an extra factor. So not all primes are odd, but all primes except 2 are.

There are 25 prime numbers from 1 to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. The first five are 2, 3, 5, 7 and 11, and the first ten end with 29. Below 10 there are four: 2, 3, 5 and 7.

Divide by prime numbers, smallest first, until only primes are left. For 90: 90 = 2 × 45, then 45 = 3 × 15, then 15 = 3 × 5, so 90 = 2 × 3 × 3 × 5, written with indices as 2 × 3² × 5. A factor tree shows the same steps as branches. Every number has exactly one set of prime factors, whichever route you take.

Give your child 12 counters and ask them to make equal rows: 2 rows of 6, 3 rows of 4. Then try 7 counters: the only ways are one row of 7 or seven rows of 1. A number like 7 that only makes those two arrangements is prime. Try 2, 3, 5 and 11 too.