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Highest common factor (HCF)
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EasyQuestion 1
[2 marks]Find the highest common factor (HCF) of 24 and 36.
Solution for Question 1
MediumQuestion 2
[3 marks]Using prime factorisation, find the HCF of 84 and 120.
Solution for Question 2
HardQuestion 3
[4 marks]A florist has 48 roses and 72 tulips. She wants to make identical bouquets using all the flowers, with no flowers left over.
(a) What is the maximum number of bouquets she can make?
(b) How many of each flower will be in each bouquet?
Solution for Question 3
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The Highest Common Factor (HCF) is the largest number that divides exactly into two or more numbers. There are two main methods: listing factors or using prime factorisation.
For smaller numbers, list all factors of each number and find the largest one they share. For example, factors of 12 are 1, 2, 3, 4, 6, 12 and factors of 18 are 1, 2, 3, 6, 9, 18. Common factors are 1, 2, 3, 6, so HCF = 6.
For larger numbers, prime factorisation is more efficient. Write each number as a product of primes, then multiply together the primes that appear in ALL numbers, using the lowest power of each. HCF is useful for simplifying fractions and solving problems about dividing items into equal groups.
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