# What is the GCF of 77 and 56?

The greatest common factor(GCF) of two numbers 77 and 56 is the maximum possible number that divides both the numbers exactly.

## Answer: GCF of 77 and 56 is 7

The greatest common factor or the greatest common divisor of two numbers is the largest possible number which divides both the numbers exactly without any remainder.

## Explanation:

The GCF of 77 and 56 can be calculated by :

- Prime factorization Method
- Listing the common factors method

### Method 1: GCF of 77 and 56 by Prime Factorization

Express 77 and 56 as a product of its prime factors

Prime factorization of 77 is 7 × 11

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

Common factor = 7

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

GCF is 7

### Method 2: GCF of 77 and 56 by Listing the Common Factors

We start with listing all the factors of 77 and 56, then identify the common factors. The highest among the common factors is the GCF of 77 and 56.

Factors of 77 are **1,** **7,** 11, 77.

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

Common Factors of 77 and 56: 1, 7

Greatest common factor= 7

GCF of 77 and 56 is 7

The solution to our question GCF of 77 and 56 is independent of the method.