Factors, multiples and primes · Grade 7
In Grade 7 you learn: prime factorisation.
Factors are numbers that divide exactly into a number; multiples are the numbers in its times table. Primes, which have exactly two factors, are the building blocks: every whole number can be written as a product of primes in just one way. HCF and LCM solve real problems about sharing and timing.
Key facts
- A factor of 12 divides into it exactly: 1, 2, 3, 4, 6, 12. Find factors in pairs.
- Multiples of 7: 7, 14, 21, 28, … (they go on for ever).
- A prime has exactly two factors, 1 and itself: 2, 3, 5, 7, 11, 13, … (1 is not prime.)
- Product of primes: use a factor tree, e.g. 60 = 2^2 × 3 × 5.
- Divisibility: by 3 if the digits add to a multiple of 3; by 4 if the last two digits are a multiple of 4.
Worked examples
Example 1
Write 60 as a product of prime factors.
Answer: 2^2 × 3 × 5