The GCF (greatest common factor) of the numbers 23 and 17 is 1

On this page we are calculating the Greatest Common Factor of 23 and 17

To change these 23 and 17 numbers, please amend the values in the fields below:

How to find the Greatest Common Factor of 23 and 17?

There are many methods we can apply to calculate the GCF of 23 and 17.

In our first method, we'll find out the prime factorisation of the 23 and 17 numbers.

In our second method, we'll create a list of all the factors of the 23 and 17 numbers.


These are the numbers that divide the 23 and 17 numbers without a remainder. These are the numbers that divide the 23 and 17 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 23 and 17.

Methods of calculating the GCF of 23 and 17:


Method 1 - Prime Factorisation

With the prime factorisation method, all we have to do is to find the common prime factors of 23 and 17, and then multiply them. Really simple:

With the prime factorisation method, all we have to do is to find the common prime factors of 23 and 17, and then multiply them. Really simple:

Step 1: Let's create a list of all the prime factors of 23 and 17:

Prime factors of 23:

As you can see below, the prime factors of 23.

Let's illustrate the prime factorization of 23 in exponential form:

23 =
231

Prime factors of 17:

As you can see below, the prime factors of 17.

Let's illustrate the prime factorization of 17 in exponential form:

17 =
171

Step 2: Write down a list of all the common prime factors of 23 and 17:

As seen in the boxes above, the common prime factors of 23 and 17 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 23 and 17, 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 23 and 17 without a remainder:

List of factors that divide 23 without a remainder are:

1 and 23

List of factors that divide 17 without a remainder are:

1 and 17

Step 2: Identify the largest common number from the 23 and 17 lists above:

As you can see in the lists of factors from above, for the numbers 23 and 17, 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 23 and 17 is 1


Method 3 - Euclidean algorithm

The Euclidean algorithm says that if number k is the GCM of 17 and 23, then the number k is also the GCM of the division remainder of the numbers 17 and 23.

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:

17, 23

Step 2

Take out, from the set, the smallers number as you divisor: 17

The remaining set is: 23

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

23 mod 17 = 6

Gather the divisor and all of the remainders and sort them in ascending order. Remove any duplicates and 0. Our set is: 6,17

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

Take out, from the set, the smallers number as you divisor: 6

The remaining set is: 17

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

17 mod 6 = 5

Gather the divisor and all of the remainders and sort them in ascending order. Remove any duplicates and 0. Our set is: 5,6

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

Take out, from the set, the smallers number as you divisor: 5

The remaining set is: 6

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

6 mod 5 = 1

Gather the divisor and all of the remainders and sort them in ascending order. Remove any duplicates and 0. Our set is: 1,5

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: 5

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

5 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 17 and 23 is 1