# What is the GCF of 30 and 45?

The highest common factor or greatest common factor of two or more numbers is the maximum possible number that divides the given numbers without any remainder i.e., 0 as remainder.

## Answer: GCF of 30 and 45 is 15

Two methods to find the GCF of 30 and 45 are explained below.

## Methods to Find GCF of 30 and 45

We can find the GCF by:

- Prime factorization
- Listing the common factors
- Long division

### Greatest Common Factor of 30 and 45 By Prime Factorization

Let us re-write 30 and 45 as a product of their prime factors using the up-side-down division method.

Prime factorization of 30: 2 × 3 × 5

Prime factorization of 45: 3 × 3 × 5

GCF or greatest common factor is the product of the prime factors that are common to each of the given numbers.

### GCF of 30 and 45 by Listing the Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30

Factors of 45: 1, 3, 5, 9, 15 and 45

Common Factors of 30 and 45: 1, 2, 3, 6, 9 and 18

GCF of 30 and 45 is 15

### Find GCF of 30 and 45 by Long Division

- Step 1: Divide 45 by 30 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

The HCF, irrespective of the method we choose, will be the same.