# What is the GCF of 32 and 45?

The highest common factor(HCF) or the greatest common factor(GCF) of two numbers 32 and 45 is the largest possible number which divides both the numbers exactly.

## Answer: GCF of 32 and 45 is 1

The greatest common factor of two numbers is the largest possible number which divides both the numbers exactly without any remainder. It is the highest of all the common factors of 32 and 45.

## Explanation:

Let us Find GCF of 32 and 45 by

- Prime factorization Method
- Listing the common factors method

### Method 1: Calculate GCF of 32 and 45 by Prime Factorization

In this method, we express 32 and 45 as a product of its prime factors.

Prime factorization of 32 is 2 × 2 × 2 × 2

Prime factorization of 45 is 3 × 3 × 5

Common factor = 1

The greatest common factor(GCF) is the product of the factors that are common to each of the given numbers.

GCF is 1

### Method 2: Calculate GCF of 32 and 45 by Listing the Common Factors

The process is that,

- We list all the factors of 32 and 45
- Identify the common factors.

The highest among the common factors is the GCF of 32 and 45.

Factors of 32 are **1,** 2, 4, 8, 16, 32

Factors of 45 are **1,** 3, 5, 9, 15, 45

Common Factors of 32 and 45: 1.

Greatest common factor= 1

GCF of 32 and 45 is 1, irrespective of the method we choose.