Factors and multiples
- A factor of a number divides into it exactly. The factors of 12 are 1, 2, 3, 4, 6 and 12.
- A multiple of a number is in its times table. The multiples of 7 are 7, 14, 21, 28…
- Find factors in pairs: 1 × 12, 2 × 6, 3 × 4.
Prime numbers
- A prime number has exactly two factors: 1 and itself. 1 is not prime.
- The primes below 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. 2 is the only even prime.
Prime factor decomposition
- Every whole number greater than 1 can be written as a product of prime factors.
- Use a factor tree: 60 = 6 × 10 = 2 × 3 × 2 × 5 = 2² × 3 × 5 (in index form).
HCF and LCM
- The highest common factor (HCF) is the biggest number that is a factor of both numbers. HCF of 12 and 18 is 6.
- The lowest common multiple (LCM) is the smallest number that is a multiple of both. LCM of 4 and 6 is 12.
- With prime factors: the HCF uses the primes they share (lowest powers); the LCM uses every prime (highest powers). A Venn diagram helps.
Using HCF and LCM
- HCF problems: sharing things into the largest possible equal groups.
- LCM problems: finding when things happen together again, such as buses that leave every 12 and 15 minutes (together again after 60 minutes).
Key terms
- Factor
- A number that divides exactly into another number.
- Multiple
- A number in the times table of another number.
- Prime number
- A number with exactly two factors: 1 and itself.
- Prime factor
- A factor that is a prime number.
- Product of prime factors
- A number written as prime numbers multiplied together.
- Index form
- Writing repeated factors as powers, such as 2³ × 5.
- Highest common factor (HCF)
- The largest number that is a factor of two or more numbers.
- Lowest common multiple (LCM)
- The smallest number that is a multiple of two or more numbers.
Practise Factors, multiples and primes (HCF and LCM): 12 questions