1.4 Highest common factors · Unit 1 Integers

1 · Teaching slidesuse ← → keys

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2 · Key words

factorA number that divides exactly into another number with no remainder.

common factorA number that is a factor of two or more numbers.

highest common factor (HCF)The largest number that is a factor of two or more numbers.

co-primeTwo numbers whose only common factor is 1.

simplifyTo write a fraction using the smallest possible whole numbers.

3 · Summary of the sectionrevise from this

A factor divides exactly into a number: the factors of 12 are 1, 2, 3, 4, 6, 12.
A common factor divides into both numbers.
The highest common factor (HCF) is the biggest of them.
Method: list the factors of the smaller number, then work downwards and stop at the first one that also divides the larger number.
If one number is a factor of the other, the HCF is the smaller number, e.g. HCF(6, 18) = 6.
Useful fact: HCF × LCM = a × b, e.g. for 8 and 12: 4 × 24 = 96 = 8 × 12.
Dividing a fraction's numerator and denominator by their HCF simplifies it in one step.

PDFPrintable worksheet All 56 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons4 videos

Factors | Common Factors | Greatest Common Factor (GCF)

American Math with Mr. J

Starts from listing factors and works up to the greatest common factor (= HCF).

Greatest Common Factor (GCF) | A Step-by-Step Guide

American Math with Mr. J

Longer guide with several worked examples if you need more practice.

Common Factors and HCF

British Corbettmaths

Uses the British “highest common factor” wording that matches the syllabus.

LCM HCF using Product of Primes

British stretchCorbettmaths

The prime-factorisation and Venn diagram method — a stretch technique beyond the listing method.

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Highest common factors