Data-driven 4IR skills development

Factors and Multiples


  • [Factor]  a number or quantity that when multiplied with another produces a given number or expression e.g factors of 3 are 1 and 3 because $1\times 3 = 3$, $x$ and $y$ are factors of $3xy$
  • [Multiple] a number  or expression that may be divided by another a certain number of times without a remainder e.g 10 is a multiple of 2 and 5, 200 is a multiple of 2, 4, 8 and 100. The expression $4x^{2}y$ is a multiple of $2, 4, x, x^2, y, xy$
  • [Prime factor] a number that is divisble by only one and itself e.g $3, 7, 11, 13, 19, 23$

Factorisation is the process of decomposing a number or an expression into a product of its prime factors.

Highest common factor and lowest common multiple

We can use prime factors to find the highest common factor (HCF) and lowest common multiple (LCM).

Highest common factor

Here are the list of prime factors of 24 and 36:

24 = 2 x 2 x 2 x 3

36 = 2 x 2 x 3 x 3

If we write down the numbers that are the same in both lists, they will give us the highest common factor of 24 and 36:

HCF of 24 and 36 is 2 x 2 x 3 = 12

Lowest common multiple

To find the lowest common multiple, we need to think about which list has the most of each factor.

24 = (2 x 2 x 2) x (3)

36 = (2 x 2)    x (3 x 3)

24 has the most 2s. (it has three 2s). And 36 has the most 3s (it has two 3s).

So the LCM of 24 and 36 is (2 x 2 x 2) x (3 x 3) = 72.

Share with:

Edzai Conilias Zvobwo is passionate about empowering Africans through mathematics, problem-solving techniques and media. As such, he founded MathsGee. Through this organisation, he has helped create an ecosystem for disseminating information, training, and supporting STEM education to all African people. A maths evangelist who teaches mathematical thinking as a life skill, Edzai’s quest has seen him being named the SABC Ambassador for STEM; he has been invited to address Fortune 500 C-suite executives at the Mobile 360 North America; was nominated to represent Southern Africa at the inaugural United Nations Youth Skills Day in New York; was invited to be a contributor to the World Bank Group Youth Summit in 2016; has won the 2014 SADC Protocol on Gender and Development award for his contribution to women’s empowerment in education; and has partnered with local and global firms in STEM interventions.

Comments are closed.