# What is the HCF of 324 and 144?

The Highest Common Factor(HCF) of two numbers is the highest possible number which divides both the numbers exactly. HCF of a and b is denoted by HCF(a, b)

## Answer: HCF of 324 and 144 is 36

We will explain two methods to find the HCF of 324 and 144

## Explanation:

The two methods that we are using to find HCF of 324 and 144 are shown below.

- HCF of 324 and 144 by Prime Factorization
- HCF of 324 and 144 by Long Division

### Method 1: Highest Common Factor of 324 and 144 by Prime Factorization

Let's write the prime factorization of 324 and 144

Prime factorization of 324 is 2 × 2 × 3 × 3 × 3 × 3

Prime factorization of 144 is 2 × 2 × 2 × 2 × 3 × 3

The common prime factors in the above prime factorization are 2, 2, 3 and 3.

The Highest common factor is the product of the prime factors that are common to each of the given numbers.

So, HCF of 324 and 144 is, 2 × 2 × 3 × 3 = 36

### Method 2: Highest Common Factor of 324 and 144 by Long Division

Step 1: Divide 144 by 324 and check the remainder. Here, we get the remainder as 36.

Step 2: Make the remainder of the above step 36 as the divisor and the divisor of the above step 144 as the dividend and perform the long division again.

Step 3: Then we get the remainder as 0, therefore the HCF of 324 and 144 is 36.

The solution of HCF of 324 and 144 will be the same from both the above methods.