Factors and multiples · Usually met around P4
Prime factorisation
Divide by 2, 3, 5… until only primes are left.
How to do it
Method
Divide by 2, 3, 5… until only primes are left
60 = 2 × 2 × 3 × 5
Another way
A factor tree
60 = 6 × 10 = 2 × 3 × 2 × 5
In full
Writing a number as primes multiplied together is its prime factorisation. Short division: try the smallest prime, 2, first; while it divides, keep dividing by 2, then try 3, 5, 7… until the answer is a prime. 60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5, and 5 is prime, so 60 = 2 × 2 × 3 × 5. A factor tree: split the number into two factors, split again any that aren't prime, until every branch ends in a prime: 60 = 6 × 10 = 2 × 3 × 2 × 5. However you split it, you get the same primes, usually written smallest first. 1 is not a prime, so it is never written in. Repeated primes can be written as powers: 2 × 2 = 2². To check, multiply the primes back: 2 × 2 × 3 × 5 = 60.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
637 = 7 × 7 × □
Show the answer and working
Answer: 13
637 ÷ 7 = 91, 91 ÷ 7 = 13, and 13 is prime.
Example 2
Which of these is 132 written as a product of primes?
- A. 2 × 6 × 11
- B. 2 × 2 × 3 × 13
- C. 2 × 2 × 3 × 11
- D. 4 × 3 × 11
Choose the right answer
Show the answer and working
Answer: C. 2 × 2 × 3 × 11
Every factor must be prime and they must make 132: 2 × 2 × 3 × 11.
Example 3
When 75 is written as a product of primes, how many primes are there, counting repeats?
Show the answer and working
Answer: 3
75 has 0 twos, 1 threes and 2 fives: 3 in all.
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