The GCF (greatest common factor) of the numbers 9 and 18 is 9

On this page we are calculating the Greatest Common Factor of 9 and 18

To change these 9 and 18 numbers, please amend the values in the fields below:

How to find the Greatest Common Factor of 9 and 18?

There are many methods we can apply to calculate the GCF of 9 and 18.

In our first method, we'll find out the prime factorisation of the 9 and 18 numbers.

In our second method, we'll create a list of all the factors of the 9 and 18 numbers.


These are the numbers that divide the 9 and 18 numbers without a remainder. These are the numbers that divide the 9 and 18 numbers without a remainder. Once we have these, all we have to do is to find the one that is the biggest common number from the 2 lists.

Now let's look at each methods, and calculate the GCF of 9 and 18.

Methods of calculating the GCF of 9 and 18:


Method 1 - Prime Factorisation

With the prime factorisation method, all we have to do is to find the common prime factors of 9 and 18, and then multiply them. Really simple:

With the prime factorisation method, all we have to do is to find the common prime factors of 9 and 18, and then multiply them. Really simple:

Step 1: Let's create a list of all the prime factors of 9 and 18:

Prime factors of 9:

As you can see below, the prime factors of 3 and 2.

Let's illustrate the prime factorization of 9 in exponential form:

9 =
32

Prime factors of 18:

As you can see below, the prime factors of 2, 3, and 2.

Let's illustrate the prime factorization of 18 in exponential form:

18 =
21 x
32

Step 2: Write down a list of all the common prime factors of 9 and 18:

As seen in the boxes above, the common prime factors of 9 and 18 are 3 and 2.

Step 3: All we have to do now is to multiply these common prime factors:

Find the product of all common prime factors by multiplying them:

32 x
= 9

Method 2 - List of Factors

With this simple method, we'll need to find all the factors of 9 and 18, factors are numbers that divide the another number without a remainder, and simply identify the common ones, then choose which is the largest one.

Step 1: Create a list of all the numbers that divide 9 and 18 without a remainder:

List of factors that divide 9 without a remainder are:

1, 3, and 9

List of factors that divide 18 without a remainder are:

1, 2, 3, 6, 9, and 18

Step 2: Identify the largest common number from the 9 and 18 lists above:

As you can see in the lists of factors from above, for the numbers 9 and 18, we have highlighted the number 9, which means that we have found the Greatest Common Factor, or GCF.

According to our calculations above, the Greatest Common Factor of 9 and 18 is 9


Method 3 - Euclidean algorithm

The Euclidean algorithm says that if number k is the GCM of 9 and 18, then the number k is also the GCM of the division remainder of the numbers 9 and 18.

We follow this procedure until the reminder is 0.

The Greatest Common Divisor is the last nonzero number.

Step 1: Sort the numbers into ascending order:

9, 18

Step 2

Take out, from the set, the smallers number as you divisor: 9

The remaining set is: 18

Find the reminder of the division between each number and the divisor

18 mod 9 = 0

Gather the divisor and all of the remainders and sort them in ascending order. Remove any duplicates and 0. Our set is: 9

Repeat the process until there is only one number in the set.

Step 3: Take the remaining number from our set

The Greatest Common Factor of 9 and 18 is 9