Factors and prime factors
A factor of a number divides it exactly with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12. A prime number has exactly two factors, 1 and itself (2, 3, 5, 7, 11…). A prime factor is a factor that is also prime.
Key idea / Key idea
Every whole number greater than 1 can be written as a product of prime factors. This is called prime factorisation, e.g. 12 = 2 × 2 × 3 = 22 × 3.
Prime factorisation
Keep dividing by the smallest prime that fits until you reach 1. A factor tree or repeated division both work.
- 18 = 2 × 3 × 3 = 2 × 32
- 24 = 2 × 2 × 2 × 3 = 23 × 3
Highest Common Factor (HCF)
The HCF of two numbers is the largest number that divides both exactly. One reliable method is to write each number as prime factors, then multiply the common prime factors.
Worked example / Worked example
Find the HCF of 24 and 36.
24 = 23 × 3 and 36 = 22 × 32.
Common factors: 22 × 3 = 4 × 3 = 12. So HCF = 12.
Remember / Remember
- 1 is a factor of every number but is not prime.
- Take the lowest power of each common prime for the HCF.
- The HCF is never larger than the smaller number.