# What is the GCF of 26 and 14?

To find the GCF (Greatest Common Factor) of two numbers, we have to determine the largest possible number which divides the two numbers exactly leaving the remainder as 0.

## Answer: GCF of 26 and 14 is 26

Lets see how to find the GCF of 26 and 14

## Explanation:

GCF of 26 and 14 will the greatest number that divides 26 and 14 exactly, that is, leaving the remainder 0

We can explain the GCF of 26 and 14 by the following two methods.

- Listing the common factors method
- Prime factorization Method

## Methods to Find GCF of 26 and 14

### GCF of 26 and 14 by Listing the Common Factors

The list of factors of 26 and 14 is shown below.

Factors of 26: 1, 2, 13, 26

Factors of 14: 1, 2, 7, 14

We can observe that the common factors of 26 and 14 are 1 and 2

The greatest common factor of 26 and 14 is 2

So, GCF of 26 and 14 is 2

### GCF of 26 and 14 by Prime Factorization

Let us express the numbers, 26 and 14 as a product of its prime factors.

Prime factorization of 26 is 2 × 13

Prime factorization of 14 is 2 × 7

The common prime factor is 2

GCF is the product of the prime factors that are common to the prime factorization of 26 and 14

GCF of 26 and 14 is 2

You can find the GCF in any of the above methods but the solution will be the same.