Stage 7 · Factors & multiples
Prime numbers
Try 2, 3, 5 and 7 in turn.
How to do it
Method
Try 2, 3, 5 and 7 in turn
91: not 2, 3 or 5; 91 ÷ 7 = 13, so 7
Another way
List the factors
Factors of 91: 1, 7, 13, 91
In full
A prime has exactly two factors: 1 and itself. 1 has only one factor, so it is neither prime nor composite, and the smallest prime is 2. For a number up to 100, try 2, 3, 5 and 7 in turn (not the number itself): even numbers divide by 2; if the digits add up to a multiple of 3 it divides by 3; ending in 0 or 5 it divides by 5; 7 you actually divide. The first that divides is the smallest prime factor; if none does, it's prime, because 11 × 11 = 121 is already past 100. You can also list all the factors or use the Sieve of Eratosthenes; the answer is the same.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Least prime factor of 44 = ?
Show the answer and working
Answer: Least prime factor of 44 = 2
Smallest prime factor of 44: try 2, 3, 5, 7 in turn: 44 is even, 44 ÷ 2 = 22, so the smallest prime factor is 2
Example 2
Least prime factor of 9 = ?
Show the answer and working
Answer: Least prime factor of 9 = 3
Smallest prime factor of 9: try 2, 3, 5, 7 in turn: 9 is odd, so not by 2; its digit sum is 9, a multiple of 3, 9 ÷ 3 = 3, so the smallest prime factor is 3
Example 3
Next prime after 19 = ?
Show the answer and working
Answer: Next prime after 19 = 23
The next prime after 19: 20: 20 is even, 20 ÷ 2 = 10; 21: its digits add up to 2 + 1 = 3, a multiple of 3, 21 ÷ 3 = 7; 22: 22 is even, 22 ÷ 2 = 11; 23 divides by none of 2, 3, 5, 7, so it's prime — the answer is 23
Example 4
Next prime after 89 = ?
Show the answer and working
Answer: Next prime after 89 = 97
The next prime after 89: 90: 90 is even, 90 ÷ 2 = 45; 91: 91 ÷ 7 = 13; 92: 92 is even, 92 ÷ 2 = 46; 93: its digits add up to 9 + 3 = 12, a multiple of 3, 93 ÷ 3 = 31; 94: 94 is even, 94 ÷ 2 = 47; 95: it ends in 5, 95 ÷ 5 = 19; 96: 96 is even, 96 ÷ 2 = 48; 97 divides by none of 2, 3, 5, 7, so it's prime — the answer is 97
Practise prime numbers in the game →Stage 7 · Factors & multiples · Free to start, unlimited questions, no download