# What is the GCF of 34 and 51?

Greatest Common Factor of 34 and 51 is the largest possible number which divides the numbers 34 and 51 exactly leaving the remainder as 0

## Answer: The GCF of 34 and 51 is 17.

## Explanation:

We can find the GCF by the following two methods.

### Methods to find GCF of 34 and 51

- Long division Method
- Prime factorization Method

### GCF of 34 and 51 by Long Division

**Step 1:**Divide 34 by 51 and check the remainder.**Step 2:**Make the remainder of the above step as the divisor and the divisor of the above step as the dividend and perform the long division again.**Step 3:**Continue till you get the remainder as 0

### GCF of 34 and 51 by Prime Factorization

We will express the numbers 34 and 51 as a product of their prime factors.

Prime factorization of 34 is 2 × 17

Prime factorization of 51 is 3 × 17

The common factor in both prime factorization = 17

GCF of 34 and 51 is the product of the prime factors that are common to the prime factorization of 34 and 51

So, GCF of 34 and 51 is 17

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