The Division Method is an easy method for finding the Highest Common Factor. You have different questions for more practicing purposes. The Division Method is one of the methods used for finding HCF. Students who feel finding the Highest Common Factors using the division method concept difficult and confusing can easily find HCF after referring to this article.

The Highest Common Factor for two or more given natural numbers is referred to as HCF. For a clear understanding of the concept, we’ve provided various questions on HCF using Division Method with a clear explanation. Practice the problems given here on How to find HCF and enhance your math skills.

Also, Refer:

- Prime Factorization
- Greatest Common Factor
- Examples of Greatest Common Factor (GCF)
- To find Highest Common Factor by using Prime Factorization Method

### How to find HCF using Division Method?

Here, you will learn how to find the HCF using Division Method. The division method is nothing but dividing the given number, simultaneously, to induce the common factors between them. The following are the steps to find Highest Common Factor using the division method,

Step 1: In this method, first we have to treat the smaller number as the divisor and the bigger number as the dividend.

Step 2: Now, Divide the given number until you get the remainder value as 0.

Step 3: We are about to get the common prime factors because the factors within the left-hand side divide all the numbers exactly. The product of those common factors is that the HCF of the given numbers.

### HCF by Division Method Examples

**Example 1: **

Find the HCF of 75 and 180 using the Division Method

**Solution:**

Given the values are 75, 180.

Now, find the factors using the division method. In the division method, first, take the small number as the divisor and the larger number as a dividend. Like as shown within the below figure,

Now, Divide the given number to get the remainder as 30. Next, again divide 75 by 30, we get the remainder as 15. Divide the 30 by 15, to get the remainder as 0.

Then, we write the prime factors, the left-hand side dividend numbers are factors.

The factors are 75, 30, and 15. But 15 is exactly divided and the remainder is 0.

Therefore, the HCF of 75 and 180 is 15.

**Example 2: **

What is the HCF of 16 and 24 using the Division Method?

**Solution:**

As given in the question, the values are 16, 24.

Now, we will write the prime factors.

In the division method, the divisor is the small number and a dividend is a large number. Let see how to divide,

So 8 is exactly the divided prime factor of 16 and 24.

Therefore, the HCF of 16 and 24 using the division method is 8.

**Example 3:**

Find the HCF of 72, 140, 256 using the division method.

**Solution: **

Given values are 72, 140, 256.

We have to write the prime factors.

The HCF of 72, 140 is 4.

The factors of 4, 256 is,

Among those two, the factor is 4.

Thus, the HCF of 72, 140, 256 using the division method is 4.

**Example 4:**

Find the Highest Common Factor of 248, 492? Using the Division Method.

**Solution:**

Given numbers are 248, and 492

First, divide the number 492 using the given smallest number 248.

Next, divide the quotient 248 with the remainder of the previous value, that is 244.

Then get the remainder value is 4, divide 244 with 4.

We get the remainder as 0, the division process end here.

So, the prime factor of 248, 492 is 4

Hence, the HCF of 248, 492 using the division method is 4.

**Example 5: **

What is the Highest Common Factor of 462, 780 using the division method?

**Solution:**

As given the values are 462, 780.

Now, we will write the prime factor using the division method.

In the division method, first, identify the smaller number and larger number because the small number is the divisor and the large number is a dividend.

Then, start the process till the remainder becomes zero.

The below figure shows how to perform division operation,

Therefore, the HCF of 780, 462 using the division method is 6.

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### FAQ’s on HCF using the Division Method

**1. How do we use Highest Common Factor?**

The HCF is used to simplify the fractions. The Highest Common Factor (HCF) or GCD is that the greatest number that divides exactly into two numbers.

**2. What are the steps of the Division Method?**

The following are the steps for finding the HCF using the division method,

Step 1: Initially, Divide the largest number by the smallest number.

Step 2: Next, take the divisor as new a dividend and remainder as the new divisor, it means divide the initial divisor by the first remainder.

Step 3: Proceed till the remainder is zero and therefore the last divisor is going to be the HCF of the given numbers.

**3. What is the Highest Common Factor?**

The Highest Common Factor of two or more numbers is nothing but the highest number among all the common factors of given numbers.