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Edexcel GCSE Maths Factors and multiples

Factors and multiples

This page covers the following topics:

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.

Prime numbers

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.

Factors

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.

Highest common factor

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.

Multiples

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.

Lowest common multiple

1

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Is the number 11 a prime number? Why?

Edexcel GCSE Maths Factors and multiples Is the number 11 a prime number? Why?
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2

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How many prime numbers are there?

Edexcel GCSE Maths Factors and multiples How many prime numbers are there?
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3

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Is 24 a factor of 144?

Edexcel GCSE Maths Factors and multiples Is 24 a factor of 144?
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4

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List the factors for the number 10.

Edexcel GCSE Maths Factors and multiples List the factors for the number 10.
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5

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Ben is hosting a social at his house and orders 32 slices of pizza. He is in doubt, however, of how many friends he can invite over such that everyone has the same amount of pizza. He can call either 3 friends, 7 friends or 15 friends over. What number of friends can he invite to the party?

Edexcel GCSE Maths Factors and multiples Ben is hosting a social at his house and orders 32 slices of pizza. He is in doubt, however, of how many friends he can invite over such that everyone has the same amount of pizza. He can call either 3 friends, 7 friends or 15 friends over. What number of friends can he invite to the party?
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6

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Find the highest common factor of 54 and 72.

Edexcel GCSE Maths Factors and multiples Find the highest common factor of 54 and 72.
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7

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Compute the highest common factor between 19 and 57.

Edexcel GCSE Maths Factors and multiples Compute the highest common factor between 19 and 57.
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8

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Samuel has decided to mend a few rips on a few old clothes. He has two pieces of cloth available to him one of which is 60 cm wide and the other is 72 cm wide. He needs to cut the two pieces of cloth into smaller pieces of equal width that are as wide as they can be. Calculate the width of the strips of cloth Samuel will cut for himself.

Edexcel GCSE Maths Factors and multiples Samuel has decided to mend a few rips on a few old clothes. He has two pieces of cloth available to him one of which is 60 cm wide and the other is 72 cm wide. He needs to cut the two pieces of cloth into smaller pieces of equal width that are as wide as they can be. Calculate the width of the strips of cloth Samuel will cut for himself.
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9

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How many multiples does 4 have?

Edexcel GCSE Maths Factors and multiples How many multiples does 4 have?
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10

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Find the first 3 common multiples of 5 and 10.

Edexcel GCSE Maths Factors and multiples Find the first 3 common multiples of 5 and 10.
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11

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How many lowest common multiples can there be between two numbers?

Edexcel GCSE Maths Factors and multiples How many lowest common multiples can there be between two numbers?
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12

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Calculate the lowest common multiple of 7 and 8.

Edexcel GCSE Maths Factors and multiples Calculate the lowest common multiple of 7 and 8.
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13

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Catarina is at the shops buying bread and cheese. She notices that 6 buns come in a packet and 8 slices of cheese in a packet. If she intends to eat a bun with a single sheet of cheese, how many of each will she need?

Edexcel GCSE Maths Factors and multiples Catarina is at the shops buying bread and cheese. She notices that 6 buns come in a packet and 8 slices of cheese in a packet. If she intends to eat a bun with a single sheet of cheese, how many of each will she need?
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