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Sometimes one may want to find an answer to the question what are common factors in Math?

Common factors of numbers, are __ factors__
that divide evenly into all of the numbers concerned.

It's the case that any pair or group of numbers, can have more than one common factor between them.

Factors of

Factors of

**1 , 2** and **4** are common factors of **8** and **12**.

Factors of

Factors of

Factors of

**1** and **3** are common factors of **9**, **15** and **45** together.

Greatest Common Factor

The "greatest common factor", is just the largest common factor that a pair or group of numbers
share.

This number can also be called the greatest common divisor, or greatest common denominator.

We can look at **18** and **24**.

To find the greatest common factor, one can list all the factors of each, and find the greatest
shared factor.

Factors of

Factors of

It can be seen that __ 6__ is the greatest common factor of

There is another method that can be used for finding the greatest common factor between two numbers,
a method involving prime factors.

The first step, is to put each number you have into "prime factor" form.

Instructions of how do so can be seen __ here__.

Then multiply the common prime factors together, and the result is the greatest common factor of the numbers concerned.

So for

Prime factor form:

In this form, **18** and **24** both share one **2** and
one **3** between them.

This sum gives the greatest common factor of **18** and **24**, which is **6**.

The greatest common factor of **36** and **52**?

Two prime factors of **2** are shared by **36** and **52**.

**2** × **2** = **4**

The greatest common factor of **36** and **52** is __ 4__.

The greatest common factor of **48** and **99**?

Only one prime factor, __ 3__, is shared by

So this alone is the greatest common factor between the numbers.

The same approach also works for finding the greatest common factor of more than 2 numbers.

The greatest common factor of **44**, **76** and **92**?

Two prime factors of **2** are shared by **44**, **76** and **92**.

**2** × **2** = **4**

The greatest common factor of **44**, **76** and **92** is __ 4__.

Coprime Numbers

When two numbers have no common factor between them other than **1**, they are known as "coprime
numbers".

Coprime numbers can also be called "relatively prime numbers" or "mutually prime numbers".

The greatest common factor of **8** and **27**?

No prime factors are shared by **8** and **27**.

So the greatest common factor between the two numbers involved is simply **1**.

It's the case that **8** and **27** are coprime numbers.

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