±«Óătv

Module 2 (M2) - Number - Multiples and factors

Part of MathsM2: Number

Multiples and Factors

A common factor is a factor that is shared by two or more numbers.

To find the highest common factor (HCF):

  • list the factors of the two numbers
  • select the highest factor on both lists.

A common multiple is a number that is a multiple of two or more numbers.

To find the lowest common multiple (LCM) of two numbers:

  • list multiples of the higher number until you get to one that is divisible by the smaller number.
Back to top

Example 1

What is the highest common

Solution

  1. List the factors of the two numbers
    • The factors of 12 are 1, 2, 3, 4, 6, 12
    • The factors of 18 are 1, 2, 3, 6, 9, 18
  2. Select the highest factor on both lists.
    • The highest number which is on both lists is 6.

Answer

The HCF is 6.

Example 2

What is the lowest common multiple of 5 and 8?

Solution

  1. List multiples of the higher number until you get to one that is divisible by the smaller number
    • 8, 16, 24, 32, 40,
    • 40 is the first multiple of 8 that is divisible by 5.

Answer

The LCM is 40.

Back to top

Question

15 is the highest common factor of 30 and another number. The other number is between 40 and 50.

What is the other number?

Question

Pens are sold in packs of 12 and notebooks in packs of 10. Suzi wants to buy the same number of pens and notebooks.

What is the least number she can buy?

Back to top

Test yourself

Back to top

More on M2: Number

Find out more by working through a topic