# What is the HCF of 36 and 90?

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

## Answer: HCF of 36 and 90 is 18

We will explain two methods to find the HCF of 36 and 90

## Explanation:

The two methods that we are using to find HCF of 36 and 90 are shown below.

- HCF of 36 and 90 by Prime Factorization
- HCF of 36 and 90 by Listing Method

### Method 1: Highest Common Factor of 36 and 90 by Prime Factorization

Let's write the prime factorization of 36 and 90

Prime factorization of 36 is 2 × 2 × 3 × 3

Prime factorization of 90 is 2 × 3 × 3 × 5

The common prime factors in the above prime factorization are 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 36 and 90 is 2 × 3 × 3 = 18

### Method 2: Highest Common Factor of 36 and 90 by Long Division

Step 1: Divide 90 by 36 and check the remainder. Here, we get the remainder as 18

Step 2: Make the remainder of the above step 18 as the divisor and the divisor of the above step 36 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 HCF (36, 90)

The solution to our question HCF of 36 and 90 is the same by both the methods.