# What is the GCF of 42, 70, and 84?

The largest possible number which divides the given numbers completely without leaving any remainder is called the GCF (Greatest Common Factor).

## Answer: GCF of 42, 70, and 84 is 14

GCF of 42, 70, and 84 is the highest number that divides 42, 70, and 84 exactly leaving the remainder 0.

## Explanation:

We will show two methods to find the highest common factor of 42, 70 and 84

We can find the GCF by the following methods

- GCF of 42, 70, and 84 by Listing the Common Factors
- GCF of 42, 70, and 42 by Prime Factorization

### Method 1: GCF of 42, 70, and 84 by Listing the Common Factors

The factors of 42, 70, and 84 are given below.

Clearly, the common factors of 42, 70, and 84 are 1, 2, 3, 4, 6 and 14

The highest common factor of 42, 70, and 84 is 14

### Method 2: GCF of 42, 70, and 84 by Prime Factorization

Let us represent 42, 70, and 70 as a product of its prime factors.

Prime factorization of 42 = 2 × 3 × 7

Prime factorization of 70 = 2 × 5 × 7

Prime factorization of 84 = 2 × 2 × 3 × 7

Observe that the common factors in the prime factorization of 42, 70, and 84 are 2 and 7

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

So, GCF of 42, 70, and 84 is 2 × 7 = 14

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