In Mathematics, the Highest Common Factor of two or more numbers is the greatest positive integer x, which divides both the given numbers. The Highest Common Factor is short is referred to as HCF. The Other Names of HCF are GCF (Greatest Common Factor), Greatest Common Divisor (GCD), and Highest Common Divisor (HCD).

Enhance your math knowledge by practicing the Example Problems Involving Highest Common Factor. HCF will lay a stronger foundation in learning all other similar math concepts and also increases your problem-solving ability. Refer to the Example Problems on finding HCF available here and get an idea of how to solve HCF Questions using various Prime Factorization methods. Be familiar with the concept and attempt the exams on different questions framed on Highest Common Factor with utmost confidence and score well.

Also, Refer:

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

### Finding HCF using Prime Factorization Examples

**Example 1: **

Find the HCF of 34 and 38 using the prime factorization method?

**Solution:**

Given the values 34, and 38.

Now, we will write the factors.

The factors of 34 are 1, 2, 17.

The factors of 38 are 1, 2, 19

The common factors are 1, 2.

Thus the HCF of given numbers is 2.

**Example 2: **

What is the Highest Common Factor (HCF) of 22, 132, 143?

**Solution:**

As given in the question, the values are 22, 132, 143.

Now, will find the highest common factor. So, first, write the common factors.

The factors of 22 are 1, 2,11

The factors of 132 are 1, 2, 3, 4, 6, 11, 12

The factors of 143 are 1, 11,13.

The common factors of 22, 132, 143 are 1, 11.

Therefore, the Highest Common factor among them is 11.

**Example 3:**

What is the HCF of three numbers are 40, 60, 45 using the Prime Factorization?

**Solution:**

As given in the question, the values are 40, 60, and 45.

Now, we can write the factors using the Prime Factorization method.

The factors of 40 are 2 x 4 x 5.

The factors of 60 are 2 x 3 x 5

The factors of 45 are 3 x 3 x 5.

The common factors of 40, 60, and 45 are 5.

Hence, the highest common factor of given numbers is 5.

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**Example 4: **

Find the HCF value of 92, 138.

**Solution: **

Given the value is 92 and 138.

Using the Prime Factorization, we will write the factors.

The factors of 92 are 2 x 2 x 23.

The factors of 138 are 2 x 3 x 23.

The common factors of 92, 138 are 2, 23.

Thus, the Highest Common Factor is 23.

**Example 5: **

Find the highest common factor (HCF) of 84 and 150 by using the prime factorization method.

**Solution: **

As given the question, the values are 84 and 150.

Now, we will write the prime factors.

The factors of 150 are 2 x 2 x 5 x 7.

The factors of 84 are 2 x 2 x 7 x 3.

The common factors are 2, 7.

Among them, Highest Common Factor is 7.

Hence, the HCF of the given number is 7.

**Example 6: **

What is the HCF value of 96, 112 using the prime factorization method?

**Solution:
**As given the values are 96, 112.

Now, we need to write the factors then only we can find the Highest Common Factor.

The factors of 96 are 2 x 2 x 2 x 2 x 2 x 3.

The factors of 112 are 2 x 2 x 2 x 2 x 7.

The Common factors are 2.

So, the HCF of 96 and 112 are 2.

### FAQ’s on HCF by Prime Factorization Method Examples

**1. What’s Highest Common Factor?**

It is the Highest of the common factor of two or more numbers.

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

The HCF is used to simplify the fractions. HCF or GCD is that the greatest number that divides exactly into two numbers.

**3. What is the formula of HCF? **

H.C.F is simply the Highest Common Factor. Let a and b be two integers. The below is the formula for finding the HCF of a and b is given as,

HCF = Product of two numbers / L.C.M of two numbers

HCF = (a x b)/ L.C.M (a,b)

Where L.C.M is the Least Common Multiple.