Multiples and factors
- The multiples of a number are in its times table: the multiples of 6 are 6, 12, 18, 24…
- The factors of a number divide into it exactly. Find them in pairs: the factors of 12 are 1 and 12, 2 and 6, 3 and 4.
Prime numbers
- A prime number has exactly two factors: 1 and itself. The primes under 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
- 1 is not prime, because it has only one factor. 2 is the only even prime.
- Every number can be written as a product of primes. Use a factor tree: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
HCF and LCM
- The highest common factor (HCF) is the biggest number that divides into both numbers: the HCF of 12 and 18 is 6.
- The lowest common multiple (LCM) is the smallest number that both numbers divide into: the LCM of 4 and 6 is 12.
- With prime factors, the HCF multiplies the primes the numbers share, and the LCM multiplies the highest power of every prime.
- LCM problems: buses every 12 minutes and trams every 8 minutes leave together again after 24 minutes.
Square and cube numbers
- Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
- Cube numbers: 1, 8, 27, 64, 125.
Key terms
- Multiple
- A number in a number's times table.
- Factor
- A number that divides into another number exactly.
- Prime number
- A number with exactly two factors: 1 and itself.
- Prime factor
- A factor that is a prime number.
- Product
- The answer when numbers are multiplied.
- Highest common factor
- The biggest number that is a factor of two or more numbers (HCF).
- Lowest common multiple
- The smallest number that is a multiple of two or more numbers (LCM).
- Square number
- A number multiplied by itself, such as 16 = 4 × 4.
- Cube number
- A number multiplied by itself twice, such as 27 = 3 × 3 × 3.