HCF or Highest Common Factor is the method of factorization which is used to find the greatest number which divides exactly the given numbers. Students who are confused about the HCF concept can make use of this article and learn the concept in depth. Know the method of finding the H.C.F from here. Know the Methods of the Highest Common Factor like Prime Factorization, Division Method, Factorization, etc. from the below sections.

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## HCF – Definition

HCF of two or more numbers is the highest common factor of the given numbers. The Highest Common Factors are found by multiplying two or more numbers. There are 3 methods to find the HCF. They are the Factorization method, prime factorization method, and division method.

### Methods of finding H.C.F | How to find HCF?

There are three methods to find the Highest Common Factors for the given numbers. They are as follows

1. Prime Factorization Method(Factor Tree Method)

2. Division Method

3. Factorization Method

Let us learn briefly about the methods of HCF.

**1. Prime Factorization Method (Factor Tree Method):**

In prime factorization, we factorize the numbers into prime numbers.

1. First check whether the given number is divisible by 2.

2. Divide until you cannot divide the number any further.

3. Now write the numbers as the product of the prime numbers.

4. The product of these common factors is the highest common factors of the given numbers.

**Example:** What is the HCF of 6 and 12?

**Solution:**

**Factors of 6:**

6 = 2 × 3

**Factors of 12:**

12 = 2 × 2 × 3

The common factors are 2 × 3 = 6

Thus the HCF of 6 and 12 is 6.

**2. Division Method: **

1. In the division method treat the smallest number as the divisor and the bigger number as the dividend.

2. Further divide the divisor by the remainder.

3. Divide the given number until you get the remainder as 0.

**Example:** What is the HCF of 12 and 18?

**Solution:**

**3. Factorization Method:**

In this factorization method, we find the greatest common factor by listing down the factors of the numbers.

1. First write the factors of all the given numbers.

2. Now look for the highest factor among the listed factors which are common for both the given numbers.

**Example:**

Find the HCF of 6, 12 and 18?

**Solution:**

Factors of 6 are 1, 2, 3, 6

Factors of 12 are 1, 2, 3, 4, 6, 12

Factors of 18 are 1, 2, 3, 6, 9, 18

The common factors are 1, 2, 3, 6

Thus the HCF of 6, 12 and 18 is 6.

### Highest Common Factor Examples

**Example 1.**

Find the HCF of 12 and 24 by the prime factorization method.

**Solution:**

Factors of 12 =** 2 × 2 × 3**

Factors of 24 = 2 × **2 × 2 × 3
**The common factors of 12 and 24 are 2 × 2 × 3

The Highest common factor is 2 × 2 = 4

**Example 2.**

Find the HCF of three numbers 10, 15, 25.

**Solution:**

We can find the HCF of 10, 15 and 25 using the factorization method.

10 = 2 × 5

15 = 3 × 5

25 = 5 × 5

The common factors are 2, 3 and **5**.

Thus the highest common factor of 10, 15 and 25 is 5.

**Example 3.**

Find the HCF of 18 and 24 by the division method.

**Solution:
**

The factors of 18 are

**1, 2, 3, 6**, 9, 18

The factors of 24 are

**1, 2, 3**, 4,

**6,**12, 24.

The common factors are 1, 2, 3,

**6**.

Among them, the highest common factors of 18 and 24 are 6.

**Example 4.**

Find the Highest Common Factor of two numbers 15, 24 by the division method.

**Solution:**

First, divide 15 and 24

15 will be the divisor and 24 will be dividend

Now the remainder will become the new divisor and 15 will become the new dividend.

Proceed till the remainder is zero and the last divisor will be the HCF of the given numbers.

Thus the HCF of 15 and 24 is 3.

**Example 5.**

Find the H.C.F. of three numbers 36, 48, 60 by prime factorization method.

**Solution:**

First we have to write the factors of the given numbers.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Now write the common factors of all three numbers.

Common factors of 36, 48, 60 = 1, 2, 3, 4, 6, 12

Thus the HCF of three numbers 36, 48, 60 is 12.

### FAQs on Method of H.C.F.

**1. How Do I find HCF?**

There are three methods to find H.C.F of two or more numbers

1. Division Method

2. Factorization method

3. Prime Factorization method

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

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

**3. What are the tricks and formulas to find HCF and LCM?**

- Two numbers are said to be co-prime if their HCF is 1.
- Product of two numbers = product of their HCF and LCM.
- HCF = HCF of Numerators/LCM of denominators
- LCM = LCM of Numerators/HCF of denominators