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Prime factorisation
AQA GCSE Mathematics practice questions with step-by-step solutions
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EasyQuestion 1
[2 marks]Write 60 as a product of its prime factors.
Give your answer in index form.
Solution for Question 1
MediumQuestion 2
[3 marks]Write 504 as a product of its prime factors.
Show your working using a factor tree or repeated division.
Solution for Question 2
HardQuestion 3
[4 marks]The prime factorisation of a number N is 2³ × 3² × 5.
(a) Work out the value of N.
(b) Find the smallest number you must multiply N by to give a perfect square.
Solution for Question 3
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Generate Unlimited QuestionsAbout Prime factorisation in AQA GCSE
Prime factorisation means writing a number as a product of its prime factors. Every number greater than 1 has a unique prime factorisation. There are two common methods: factor trees and repeated division.
For factor trees, split the number into any two factors, then split those factors, continuing until all branches end in primes. For repeated division, divide by the smallest prime that works, and keep dividing until you reach 1.
In AQA GCSE Maths, you should write your answer using index notation. For example, 72 = 2 × 2 × 2 × 3 × 3 should be written as 72 = 2³ × 3². Prime factorisation is essential for finding HCF and LCM efficiently.
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