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Greatest Common Factor Calculator
Welcome to our Greatest Common Factor Calculator page.
This calculator will tell you the greatest common factor between two or more numbers.
You can also use the calculator for finding all the factors of any given number.
Greatest Common Factor Calculator
Input any number values into our Greatest Common Factor Calculator and it will find quickly find all of the factors including the greatest common factor.
The Greatest Common Factor (GCF) is the largest factor that a pair or group of numbers have in common.
It can also be called the Greatest Common Denominator (GCD), the Highest Common Factor (HCF), and the Greatest Common Divisor (GCD)
The Greatest Common Factor of 32, 48 and 20 is 4 because 4 is the largest number that divides into all the numbers.
Simply type in your numbers into the space below with a SPACE after each one!
WORKING OUT
Greatest Common Factor Uses
One of the main uses of the greatest common factor is to help simplify fractions quickly.
If you type in the numerator and denominator of a fraction, the calculator will tell you the GCF.
You can then quickly simplify the fraction by dividing both the numerator and denominator by the GCF in one quick go!
Greatest Common Factor Calculator Examples
We have also included a couple of quick examples so you can see how it works...
Examples
Example 1) Find the greatest common factor of 148 and 64.
- Factors of 148: 1, 2, 4, 37, 74, 148
- Factors of 64: 1, 2, 4, 8, 16, 32, 64
As both numbers are even, we can see that 2 would be a factor of both numbers.
However, both numbers are also divisible by 4 which is the highest common factor.
The Greatest Common Factor is 4.
Example 2) Find the greatest common factor of 47 and 86.
- Factors of 47: 1, 47
- Factors of 86: 1, 2, 43, 86
In this case, the numbers have no common factor apart from 1.
These numbers are said to be coprime as their only common factor is 1.
The Greatest Common Factor is 1.
Example 3) Find the highest common factor of 144 and 78.
- Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
- Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
Both these numbers are even, so 2 is a common factor.
However, you will notice that when you add up the digits of both these numbers, the sum is divisible by 3, so 3 is a common factor.
Because both 2 and 3 are common factors, 6 must also be a common factor.
There are no larger factors, so this makes 6 the highest common factor.
The Greatest Common Factor is 6.
More Recommended Math Worksheets
Take a look at some more of our worksheets similar to these.
Greatest Common Factor Worksheets
As well as our calculator, we also have a range of greatest common factor worksheets.
These sheets have been designed for 6th and 7th grade students.
They will help students learn and practice finding the greatest common factor of numbers up to 100.
Greatest Common Factor Help
If you want to learn more about the Greatest Common Factor and how each of the methods above works, come and visit our Definition of Greatest Common Factor page.
We have lots of worked examples showing you how to find the greatest common factor using different methods.
Least Common Multiple Calculator
Our Least Common Multiple Calculator will find the lowest common multiple of 2 or more numbers.
It will also show you the working out using a choice of two different methods.
There are also some worked examples.
Multiples and Factors Worksheets
These sheets are all about finding multiples and factors of different numbers.
They are a great way to introduce multiples and factors and to practice this skill.
Sieve of Erastosthenes
The Sieve of Erastosthenes is a method for finding what is a prime numbers between 2 and any given number.
Eratosthenes was a Greek mathematician (as well as being a poet, an astronomer and musician) who lived from about 276BC to 194BC.
If you want to find out more about his sieve for finding primes, and print out some Sieve of Eratosthenes worksheets, use the link below.
Want to find out more about primes?
Take a look at our Prime Number page which clearly describes what a prime numbers is and what they are not.
There are also many different questions about prime numbers answered, as well as information about the density of primes.
Looking for more math calculators?
We have a wide range of free math calculators to help you.
Most of our calculators show you their working out so that you can see exactly what they have done to get the answer.
Our calculator hub page contains links to all of our calculators!
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Follow these 3 steps to get your worksheets printed perfectly!
How to Print or Save these sheets 🖶
Need help with printing or saving?
Follow these 3 steps to get your worksheets printed perfectly!
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