Factors and multiples · Usually met around P4
Prime and composite 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 number 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 (but not the number itself). Even numbers divide by 2. If the digits add up to a multiple of 3, it divides by 3. If it ends in 0 or 5, it divides by 5. For 7, you have to actually divide. The first one that divides is the smallest prime factor. If none of them divides, the number is prime, because 11 × 11 = 121 is already past 100. You can also list all the factors, or use the Sieve of Eratosthenes.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Next prime after 60 = ?
Show the answer and working
Answer: Next prime after 60 = 61
The next prime after 60: 61 divides by none of 2, 3, 5, 7, so it's prime — the answer is 61
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 34 = ?
Show the answer and working
Answer: Next prime after 34 = 37
The next prime after 34: 35: it ends in 5, 35 ÷ 5 = 7; 36: 36 is even, 36 ÷ 2 = 18; 37 divides by none of 2, 3, 5, 7, so it's prime — the answer is 37
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