# What is the HCF of 54, 288, and 360?

HCF (Greatest Common Factor) of three numbers is the largest number that divides the three numbers exactly leaving the remainder 0

## Answer: HCF of 54, 288, and 360 is 18

Let us see how to find the HCF of 54, 288, and 360

## Explanation:

We can find the HCF by any of the following two methods.

- Listing the common factors method to find HCF of 54, 288, and 360
- Prime factorization Method to find HCF of 54, 288, and 360

### Method 1: HCF of 54, 288, and 360 by Listing the Common Factors

The factors of 54, 288, and 360 are shown below.

The common factors of 54, 288, and 360 are 1, 2, 3, 9, and 18

Clearly, the highest common factor is 18

So, HCF of 54, 288, and 360 is 18

### Method 2: HCF of 54, 288, and 360 by Prime Factorization

We will represent 54, 288, and 360 as a product of their prime factors.

Prime factorization of 54 is 2 × 3 × 3 × 3

Prime factorization of 288 is 2 × 2 × 2 × 2 × 2 × 3 × 3

Prime factorization of 360 is 2 × 2 × 2 × 3 × 3 × 5

Common prime factors = 2 × 3 × 3

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

HCF of 54, 288, and 360 is 18

Irrespective of the method, the solution to our question HCF of 54, 288, and 360 is the same.