The GCF (greatest common factor) of the numbers 9 and 19 is 1

On this page we are calculating the Greatest Common Factor of 9 and 19

To change these 9 and 19 numbers, please amend the values in the fields below:

How to find the Greatest Common Factor of 9 and 19?

There are many methods we can apply to calculate the GCF of 9 and 19.

In our first method, we'll find out the prime factorisation of the 9 and 19 numbers.

In our second method, we'll create a list of all the factors of the 9 and 19 numbers.


These are the numbers that divide the 9 and 19 numbers without a remainder. These are the numbers that divide the 9 and 19 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 19.

Methods of calculating the GCF of 9 and 19:


Method 1 - Prime Factorisation

With the prime factorisation method, all we have to do is to find the common prime factors of 9 and 19, 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 19, and then multiply them. Really simple:

Step 1: Let's create a list of all the prime factors of 9 and 19:

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 19:

As you can see below, the prime factors of 19.

Let's illustrate the prime factorization of 19 in exponential form:

19 =
191

Step 2: Write down a list of all the common prime factors of 9 and 19:

As seen in the boxes above, the common prime factors of 9 and 19 are .

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:

= 1

Method 2 - List of Factors

With this simple method, we'll need to find all the factors of 9 and 19, 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 19 without a remainder:

List of factors that divide 9 without a remainder are:

1, 3, and 9

List of factors that divide 19 without a remainder are:

1 and 19

Step 2: Identify the largest common number from the 9 and 19 lists above:

As you can see in the lists of factors from above, for the numbers 9 and 19, we have highlighted the number 1, which means that we have found the Greatest Common Factor, or GCF.

According to our calculations above, the Greatest Common Factor of 9 and 19 is 1


Method 3 - Euclidean algorithm

The Euclidean algorithm says that if number k is the GCM of 9 and 19, then the number k is also the GCM of the division remainder of the numbers 9 and 19.

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, 19

Step 2

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

The remaining set is: 19

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

19 mod 9 = 1

Gather the divisor and all of the remainders and sort them in ascending order. Remove any duplicates and 0. Our set is: 1,9

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

Take out, from the set, the smallers number as you divisor: 1

The remaining set is: 9

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

9 mod 1 = 0

Gather the divisor and all of the remainders and sort them in ascending order. Remove any duplicates and 0. Our set is: 1

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 19 is 1