# What is the GCF of 17 and 51?

GCF or the greatest common factor of two numbers 17 and 51 is the largest possible number that divides both the numbers exactly.

## Answer: GCF of 17 and 51 is 17.

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

## Explanation:

We can find the GCF of the numbers in many ways the commonly used methods are listed below.

- Calculate GCF of 17 and 51 by Prime Factorization
- Calculate GCF of 17 and 51 by Listing the Common Factors

### Method 1: Calculate GCF of 17 and 51 by Prime Factorization

In this method, we represent 17 and 51 as a product of its prime numbers

Prime factorization of 17 is 17

Prime factorization of 51 is 3 × 17

Common factor = 17

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

GCF is 17

### Method 2: Calculate GCF of 17 and 51 by Listing the Common Factors

In this method, we list all the factors of 17 and 51, then identify the common factors.

The highest among the common factors is the GCF of 17 and 51.

Factors of 17: 1, 17 as it is a prime number

Factors of 51: 1, 3, 17, 51

Common Factors of 17 and 51: 1, 17

Greatest common factor= 17

GCF of 17 and 51 is 17

GCF of 17 and 51 is unique and is the same as 17 always, irrespective of the method we choose to find GCF.