The GCF (greatest common factor) of the numbers 22 and 35 is 1

On this page we are calculating the Greatest Common Factor of 22 and 35

How to find the Greatest Common Factor of 22 and 35?

There are many methods we can apply to calculate the GCF of 22 and 35.

In our first method, we'll find out the prime factorisation of the 22 and 35 numbers.

In our second method, we'll create a list of all the factors of the 22 and 35 numbers.

These are the numbers that divide the 22 and 35 numbers without a remainder. These are the numbers that divide the 22 and 35 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 22 and 35.

Methods of calculating the GCF of 22 and 35:

Prime Factorisation
List of factors
Euclidean algorithm
Binary Greatest Common Divisor algorithm

Method 1 - Prime Factorisation

With the prime factorisation method, all we have to do is to find the common prime factors of 22 and 35, and then multiply them. Really simple:

Step 1: Let's create a list of all the prime factors of 22 and 35:

Prime factors of 22:

As you can see below, the prime factors of 2 and 11.

Let's illustrate the prime factorization of 22 in exponential form:

22 =

2¹ x

11¹

Prime factors of 35:

As you can see below, the prime factors of 5 and 7.

Let's illustrate the prime factorization of 35 in exponential form:

35 =

5¹ x

7¹

Step 2: Write down a list of all the common prime factors of 22 and 35:

As seen in the boxes above, the common prime factors of 22 and 35 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 22 and 35, 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 22 and 35 without a remainder:

List of factors that divide 22 without a remainder are:

1, 2, 11, and 22

List of factors that divide 35 without a remainder are:

1, 5, 7, and 35

Step 2: Identify the largest common number from the 22 and 35 lists above:

As you can see in the lists of factors from above, for the numbers 22 and 35, 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 22 and 35 is 1

Method 3 - Euclidean algorithm

The Euclidean algorithm says that if number k is the GCM of 22 and 35, then the number k is also the GCM of the division remainder of the numbers 22 and 35.

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:

22, 35

Step 2

Take out, from the set, the smallers number as you divisor: 22

The remaining set is: 35

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

35 mod 22 = 13

Gather the divisor and all of the remainders and sort them in ascending order. Remove any duplicates and 0. Our set is: 13,22