GCSE Maths (AQA)

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HCF & Prime Factorisations

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Number Structure and Calculation

HCF & Prime Factorisations

4:12 HCF & LCM
Spec N4
Previous Highest Common Factor Next Lowest Common Multiple
  • The highest common factor (HCF) can be found using prime factor trees and Venn diagrams.
  • Prime factors are any primes that divide evenly into a number.
  • Venn diagrams are a way of sorting data into groups called sets.
  • In a Venn diagram, any number that goes inside both circles is written once in the intersection.
  • The HCF is the product of all the numbers in the intersection of the Venn diagram.
  • Other techniques can be used to find the HCF, but Venn diagrams are useful for visualizing the problem.
  • To find the HCF of more than two numbers, draw more than two intersecting circles.
  • Example: Find the HCF of 60 and 72.
  • Step 1: Find the prime factorization of 60 using a factor tree.
  • Step 2: Find the prime factorization of 72 using a factor tree.
  • Step 3: Complete a Venn diagram with the prime factors of 60 and 72.
  • Step 4: Find the HCF by multiplying the numbers in the overlap of the Venn diagram.
  • The HCF of 60 and 72 is 12.

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