Q-files is free to read thanks to advertising. To enjoy the site completely ad-free, please subscribe. Learn more →

About Q-files Contact Us Menu
Advertisement

EASY READ Numbers

What are the multiples of a number?

A multiple is the number you get when you multiply a certain number by another one. For example, the multiple of 2 when you multiply it by 3 is 6. The factors of a number are the numbers it can divide into exactly. So the factors of 6 are 2 and 3.

Multiples
Multiples

Multiples

A multiplication tables grid
A multiplication tables grid

The multiples of a number are any number we get by multiplying it by another number.

For example, the multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 and so on.

Multiples of 2 are always even numbers. So, if a number is even (it ends with a 2, 4, 6, 8 or 0), we know it is a multiple of 2.

Multiples of 5 always end with 0 or 5. These are: 5, 10, 15, 20, 25, 30, 35, 40 and so on.
​​​​​​​
So we can tell that the number 1490 is a multiple of 5, because it ends with a 0.

Factors

The factors of a number are the numbers it can divide into exactly.

If 10 is the multiple of 2 and 5, then 2 and 5 are both factors of 10. 1 and 10 are also factors of 10 since 1 × 10 = 10.​​​​​​​

​​​​​​​Factor pairs are a set of two factors, which, when multiplied together, produce the original number. For 10, these are:

1 x 10 = 10       2 x 5 = 10

Using factor rainbows to work out factor pairs
Using factor rainbows to work out factor pairs
Common factors of 8 and 12
Common factors of 8 and 12

Common factors

If a factor is shared by two or more numbers, it is called a common factor. One way of finding the common factors of two numbers is to list the factors for each, and see which ones appear in both lists.

For example, to find the common factors of 8 and 12:

Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12

So the common factors of 8 and 12 are 1, 2 and 4.​​​​​

Advertisement

Prime numbers

This ancient method for finding prime numbers is called the Sieve of Erastothenes. Here it is used to find all the prime numbers up to 120. First it finds all the multiples of 2 (red), then 3 (green), 5 (blue) and 7 (yellow). The remaining numbers (highlighted at the end in pink) are prime.
This ancient method for finding prime numbers is called the Sieve of Erastothenes. Here it is used to find all the prime numbers up to 120. First it finds all the multiples of 2 (red), then 3 (green), 5 (blue) and 7 (yellow). The remaining numbers (highlighted at the end in pink) are prime.

Some numbers have only two factors: 1 and themselves. These are prime numbers. 1 is not a prime number, because it only has one factor. 

9 is not a prime number because it can be divided by 3 as well as 1 and itself.

15 is not a prime number because it can be divided by 3 and 5 as well as 1 and itself.

17 is a prime number because it can only be divided by 1 and 17.

The first eight prime numbers are: 2, 3, 5, 7, 11, 13, 17 and 19. But there are many more prime numbers larger than these. A computer can be used to test extremely large numbers to see if they are prime. The largest known prime number has 24,862,048 digits.

Prime factors

If a factor happens to be a prime number, it is called a prime factor. To find the common prime factors of two numbers, list the prime factors for each and see which appear in both lists.

Finding common prime factors can help us to find the highest common factor of two numbers (the highest number they can both divide into). You can find it by multiplying the common prime factors of any two numbers. In this example, the common prime factors of 24 and 30 are 2 and 3 (5 is a prime factor of 30 but not of 24).

2 x 3 = 6

So the highest common factor that 24 and 30 can both divide into is 6.

Finding the common prime factors of 24 and 30
Finding the common prime factors of 24 and 30

Consultant: Adam Larking

Key words

common factor a factor shared by two or more numbers

factor the numbers that a number can divide into exactly (without any left over)

factor pairs a pair of factors which produce the original number when multiplied together

multiple the number you get when you multiply one number by another

prime number a number which only has two factors: 1 and itself
Advertisement

pics

This ancient method for finding prime numbers is called the Sieve of Erastothenes. Here it is used to find all the prime numbers up to 120. First it finds all the multiples of 2 (red), then 3 (green), 5 (blue) and 7 (yellow). The remaining numbers (highlighted at the end in pink) are prime.
To find the common prime factors of 24 and 30, we list all the factors for each number, and circle the ones that are prime. The prime numbers that appear on both lists (circled in yellow) are the common prime factors.
The multiples of 2 up to 10
You can use factor rainbows to work out factor pairs. Each colour on the rainbow links two numbers in a factor pair.
Listing the factors of 8 and 12 to find their common factors (factors that they both have, or "have in common").
When we multiply a number by another, we get multiples.
A multiplication tables grid. The coloured columns of numbers under the first row are the multiples of the top row number. For example, the red column shows the multiples of 8.

Without in any way limiting Q-files Ltd’s exclusive rights under copyright, any use of this publication to “train” generative artificial intelligence (AI) technologies to generate text is expressly prohibited. Q-files Ltd reserves all rights to license use of this work for generative AI training and development of machine learning language models.