Factors & Multiples

5 minQuiz at the end

Factors

Factors of a number divide it exactly (with no remainder).

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factor pairs of 24: (1,24), (2,12), (3,8), (4,6)

Multiples

Multiples are what you get when you multiply a number by 1, 2, 3, 4, …

Multiples of 7: 7, 14, 21, 28, 35, 42, 49…

Highest Common Factor (HCF)

The HCF of two numbers is the largest factor they share.

Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18

HCF(12, 18) = 6

Lowest Common Multiple (LCM)

The LCM is the smallest multiple shared by two numbers.

Multiples of 4: 4, 8, 12, 16, 20… Multiples of 6: 6, 12, 18, 24…

LCM(4, 6) = 12

Prime Factorisation

Every composite number can be written as a product of prime factors.

Factor tree for 36:

     36
    /  \
   4    9
  / \  / \
 2  2  3  3

36 = 2 Γ— 2 Γ— 3 Γ— 3 = 2Β² Γ— 3Β²

Using HCF and LCM

  • HCF β†’ simplifying fractions, sharing into equal groups
  • LCM β†’ adding/subtracting fractions, finding common denominators, scheduling problems