# What is the GCF of 14 and 56?

GCF (Greatest Common Factor) of two numbers is the largest possible number that divides the two numbers exactly without leaving any remainder.

## Answer: GCF of 14 and 56 is 14

GCF of 14 and 56 is the highest number that divides 14 and 56 exactly leaving the remainder 0.

## Explanation:

We can find the GCF by the following methods.

- Prime factorization Method
- Listing the common factors method

### Method 1: Calculate GCF of 14 and 56 by Prime Factorization

Let us represent 14 and 56 as a product of its prime factors.

- Prime factorization of 14 is 2 × 7
- Prime factorization of 56 is 2 × 2 × 2 × 7

The common factors in the prime factorization of 14 and 56 are 2 and 7.

GCF is the product of the factors that are common to each of the given numbers.

So, GCF of 14 and 56 is 14.

### Method 2: Calculate GCF of 14 and 56 by Listing the Common Factors

The factors of 14 and 56 are shown below.

Factors of 14: 1, 2, 7, __14__

Factors of 56: 1, 2, 4, 7, 8, ** 14**, 28, 56

Clearly, the common factors of 14 and 56 are 1, 2, 7 and 14.

The highest common factor of 14 and 56 is 14.

Thus GCF(14, 56) is 14.

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