Prime Factor Decomposition (Cambridge (CIE) IGCSE Maths) : Revision Note

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Prime Factor Decomposition

What are prime factors?

  • A factor of a given number is a value that divides the given number exactly, with no remainder

    • e.g. 6 is a factor of 18

  • prime number is a number which has exactly two factors; itself and 1

    • e.g. 5 is a prime number, as its only factors are 5 and 1

    • You should remember the first few prime numbers:

      • 2, 3, 5, 7, 11, 13, 17, 19, …

  • The prime factors of a number are therefore all the primes which multiply to give that number

    • e.g. The prime factors of 30 are 2, 3, and 5

      • 2 × 3 × 5 = 30

How do I find prime factors?

  • Use a factor tree to find prime factors

    • Split the number up into a pair of factors

    • Then split each of those factors up into another pair

    • Continue splitting up factors along each "branch" until you get to a prime number

      • These can not be split into anything other than 1 and themselves

      • It helps to circle the prime numbers at the end of the branches

Prime factors of 360 in a factor tree
  • A number can be uniquely written as a product of prime factors

    • Write the prime factors as a multiplication, in ascending order

      • 360 = 2 × 2 × 2 × 3 × 3 × 5

    • This can then be written more concisely using powers

      • 360 = 23 × 32 × 5

  • A question asking you to do this will usually be phrased as "Express … as the product of its prime factors"

Worked Example

Write 432 as the product of its prime factors.

Create a factor tree
Start with 432 and choose any two numbers that multiply together to make 432

igcse-core-maths-oct-19-paper-3-q4g-1

Repeat this for the two factors, until all of the values are prime numbers and cannot be broken down any further

igcse-core-maths-oct-19-paper-3-q4g-2

The answer will be the same regardless of the factors chosen in the first step

Write the prime numbers out as a product

432 equals space 2 space cross times space 2 space cross times space 2 space cross times space 2 space cross times space 3 space cross times space 3 space cross times space 3

Any repeated prime factors can be written as a power

432 space equals space bold 2 to the power of bold 4 bold space bold cross times bold space bold 3 to the power of bold 3 bold space 

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Jamie Wood

Author: Jamie Wood

Expertise: Maths Content Creator

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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