# How to find the HCF of 20, 30, and 40?

HCF of two numbers 20, 30, and 40 is the largest possible number which divides both the numbers exactly.

## Answer: HCF of 20, 30, and 40 is 10

## Explanation:

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

We can find the HCF by the following methods

- Prime factorization Method
- Listing the common factors method
- Long division Method

### Method 1: HCF of 20, 30, and 40 by Prime Factorization

Let us represent 20, 30, and 40 as a product of its prime numbers

Prime factorization of 20 is 2 x 2 x 5

Prime factorization of 30 is 2 x 3 x 5

Prime factorization of 40 is 2 x 2 x 2 x 5

Common factor = 2, 5

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

HCF is 2 x 5 = 10

### Method 2: HCF of 20, 30, and 40 by Long Division

- Step 1: Divide 40 by 20 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

- Step 4: Note down the highest common factor of 40 and 20.
- Step 5: Now divide the remaining number 30 by HCF(40, 20) i.e., 20
- Step 6: Divide 30 by 20 and check the remainder.
- Step 7: 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 8: Continue till you get the remainder as 0

You can find the HCF in any of the above methods but the solution will be the same.