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Factors, multiples and primes
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Factors and multiples help you simplify fractions, find common denominators and solve timing puzzles.
Key words
A factor divides exactly into a number: the factors of 12 are 1, 2, 3, 4, 6, 12.
A multiple is in the number's times table: multiples of 12 are 12, 24, 36, ...
A prime number has exactly two factors, 1 and itself: 2, 3, 5, 7, 11, 13, ...
1 is not prime (it has only one factor).
A multiple is in the number's times table: multiples of 12 are 12, 24, 36, ...
A prime number has exactly two factors, 1 and itself: 2, 3, 5, 7, 11, 13, ...
1 is not prime (it has only one factor).
Prime factorisation
Every whole number greater than 1 is either prime or a product of primes. Use a factor tree.
60 = 2 × 2 × 3 × 5 = 22 × 3 × 5
60 = 2 × 2 × 3 × 5 = 22 × 3 × 5
HCF and LCM
The highest common factor (HCF) is the biggest number that divides into both.
The lowest common multiple (LCM) is the smallest number in both times tables.
HCF of 12 and 18 is 6. LCM of 12 and 18 is 36.
The lowest common multiple (LCM) is the smallest number in both times tables.
HCF of 12 and 18 is 6. LCM of 12 and 18 is 36.
Find the HCF and LCM of 12 and 18.
- 12 = 22 × 3 and 18 = 2 × 32
- HCF: primes they share, 2 × 3 = 6
- LCM: 22 × 32 = 36
Answer: HCF 6, LCM 36
Factors divide in, multiples are in the times table, primes have exactly two factors. HCF is the biggest shared factor, LCM the smallest shared multiple.
The interactive lesson includes the diagrams for this topic.
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