number · Year 7 · Suggested learning sequence
Prime factorisation
Every whole number bigger than 1 can be written as a product of prime numbers in exactly one way. Split the number into any factor pair, then keep splitting each branch until every end is prime. Collect all the primes at the ends, including repeats, and write them smallest first: 60 = 2 × 2 × 3 × 5. Index notation groups repeats: 2 × 2 × 2 is 2³, which means 2 multiplied by itself three times.
Sample questions
Write 90 as a product of prime factors, smallest first.
- The circled numbers at the ends of the branches are prime: 2, 3, 3, 5.
- Write every circled number, including repeats, from smallest to largest, joined by ×.
- 90 = 2 × 3 × 3 × 5
Answer: 2 × 3 × 3 × 5
Write 126 as a product of prime factors, smallest first.
- The circled numbers at the ends of the branches are prime: 2, 3, 3, 7.
- Write every circled number, including repeats, from smallest to largest, joined by ×.
- 126 = 2 × 3 × 3 × 7
Answer: 2 × 3 × 3 × 7
Write 147 as a product of prime factors, smallest first.
- The circled numbers at the ends of the branches are prime: 3, 7, 7.
- Write every circled number, including repeats, from smallest to largest, joined by ×.
- 147 = 3 × 7 × 7
Answer: 3 × 7 × 7