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Factors and multiples for OCR GCSE Maths
This page covers the following topics:
1. Prime numbers
2. Factors
3. Highest common factor
4. Multiples
5. Lowest common multiple
Prime numbers are a special group of numbers that only have two factors. That is, prime numbers are numbers that can only be divided perfectly by two distinct numbers: 1 and themselves.
A factor is a whole number, an integer, that divides another number exactly. Factors can be identified by discovering factor pairs of a number which are numbers that when multiplied together produce the number being inspected. For example, 1 and 24, 2 and 12, 3 and 8, and 4 and 6 are all factor pairs of 24 which means that the list of factor of 24 is 1, 2, 3, 4, 6, 8, 12 and 24.
Highest common factor (HCF) is the largest common factor between two or more numbers.
To find the HCF between two numbers, a tree diagram can be used to break down numbers into their prime factors and calculate the product of the common prime factors of both numbers. Prime factors are the smallest prime numbers that when multiplied produce the number being inspected.
Alternatively, use a Venn diagram to list the prime factors of the two numbers to find their HCF as the product of the common prime factors of both numbers.
Multiples refer to the numbers in the times table of any number. For example, 15 is a multiple of 5 and it is also a multiple of 3. 15 can, then, be said to be a common multiple of 5 and 3.
Lowest common multiple (LCM) is the smallest common multiple between two numbers.
To find the LCM between two numbers, you may use a tree diagram to break down numbers into their prime factors and calculate the product of both the highest common factor (HCF) and the prime factors left behind after calculating the HCF.
Prime factors are the smallest prime numbers that when multiplied produce the number being inspected.
Alternatively, use a Venn diagram to list the prime factors of the two numbers to find the LCM as the product of the numbers in all sections of the Venn diagram.
1
Is 250 a common multiple of 17 and 5?
250 is divisible by 5 but not by 17.
no
2
Harim has saved £67 and he would like to use this money to donate equally as much as possible to 4 charities. All of these charities accept only whole-pound amounts. How much of what Harim has saved will be leftover after the donations?
64 is the next largest number that fits into 67 and is divisible by 4.
67 − 64 = 3
Therefore, Harim will have £3 leftover.
£3
3
How many prime numbers are there?
The only condition is that the number be divisible by 1 and itself.
an infinite amount
4
Find the highest common factor of 54 and 72.
Breaking 54 down to its prime factors gives 2, 3, 3, 3.
Breaking 72 down to its prime factors gives 2, 2, 2, 3, 3.
The common prime factors are 2, 3, 3.
HCF = 2 × 3 × 3 = 18
18
5
Is 8 the highest common factor between 16 and 48?
16 is the highest common factor.
no
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