Prime Factor Decomposition - GCSE Maths Definition

What is prime factor decomposition?

In GCSE maths, the process of writing a number as a product of its prime factors is known as prime factor decomposition. For example, the prime factor decomposition of 30 would be 2×3×5.

Some numbers may have a prime factor which is repeated in its product of prime factors. For example the prime factor decomposition of 40 is 2×2×2×5. This can be written more concisely using powers as 2³×5.

How do I find the prime factor decomposition of a number?

You can use a "factor tree" to find prime factors. This works by writing the number at the top and splitting this up into any two factors (they do not need to be prime), and writing them down at the end of the "branches".

Repeat this process for the numbers at the end of each branch, until you reach a prime number. Remember that a prime number only has two factors; 1 and itself. It is helpful to circle prime factors when they appear in the tree.

An example factor tree is shown below for 360. It can be seen that the prime factor decomposition for 360 is 2×2×2×3×3×5 or 2³×3²×5.

A prime factor decomposition for a number is unique. For example, the only way to write 360 in prime factor decomposition form is as the product of three 2's, two 3's and one 5.

What is prime factor decomposition used for?

Once prime factor decomposition has been used to write a number as a product of primes, this can be used to:

• Tell if a number is a square or cube number

• Find the square root of a square number

• Find the square root of any number in an exact form

• Find the HCF and LCM of a pair of numbers

You can learn how to do the above by reading our revision notes on prime factor decomposition and HCF & LCM.

Prime factor decomposition revision resources to ace your exams

Learn more about prime factor decomposition with our revision notes. To test your knowledge, try our prime factors, HCF & LCM exam questions.

For quick-fire GCSE maths revision use our collection of interactive flashcards for GCSE maths. We also have past papers for your exam practice.

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