# What is the GCF of 30 and 105?

GCF (Greatest Common Factor) of two numbers is the largest possible number which divides the two numbers exactly without any remainder.

## Answer: GCF of 30 and 105 is 15

We will explain two methods to find the GCF of 30 and 105

## Explanation:

The two methods that we are using to find GCF of 30 and 105 are shown below.

- GCF of 30 and 105 by Long Division
- GCF of 30 and 105 by Prime Factorization

### Method 1: GCF of 105 and 30 by Long Division

**Step 1: **Divide 105 by 30 and check the remainder. Here, we get the remainder as 15.

**Step 2: **Make the remainder 15 as the divisor and the divisor 30 as the dividend and perform the long division again.

**Step 3: **Continue till you get the remainder as 0 and the last divisor is the GCF of 30 and 105

Since the remainder is 0 in the second step, therefore the GCF of 105 and 30 is 15.

### Method 2: GCF of 30 and 105 by Prime Factorization

We will represent 30 and 105 as a product of their prime factors.

Prime factorization of 30 is 2 × 3 × 5

Prime factorization of 105 is 3 × 5 × 7

Common prime factors are 3 and 5.

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

GCF of 30 and 105 is 3 × 5 = 15.

Irrespective of the method, the solution to our question GCF of 30 and 105 is the same.