# What is the GCF of 27 and 45?

The largest possible number which divides the given numbers exactly without any remainder is called as its Greatest Common Factor

## Answer: GCF of 27 and 45 is 9

The GCF (greatest common factor) is the same as: HCF (Highest Common Factor), GCD (Greatest Common Divisor), HCD (Highest Common Divisor), GCM (Greatest Common Measure), HCM (Highest Common Measure)

## Explanation:

Two methods to find the GCF of 27 and 45 are explained below.

### Methods to find GCF of 27 and 45

- GCF of 27 and 45 by Prime Factorization
- GCF of 27 and 45 by Long Division

### Method 1: Prime Factorization to Obtain GCF of 27 and 45

Let us represent 27 and 45 as a product of its prime factors.

Prime factorization of 27 is 3 × 3 × 3

Prime factorization of 45 is 3 × 3 × 5

Common factors = 3 and 3

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

GCF is 9

### Method 2: Long Division to Obtain GCF of 27 and 45

- Step 1: Divide 45(number which is larger) by 27(number which is smaller) 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 the division till you get remainder as zero.

By both the methods we arrive at the same answer.