**Created By :**
Jatin Gogia

**Reviewed By :**
Rajasekhar Valipishetty

**Last Updated :**
Apr 06, 2023

Make use of the HCF Calculator provided here and calculate the highest common factor for the given numbers. Just enter your numbers in the below input box and then click on the Calculate button to get the accurate HCF Solution for the entered integers.

**Ex: **HCF of 25, 40, 45 (or) HCF of 24, 96, 16 (or) HCF of 78, 98, 108

**Here are some samples of HCF Numbers calculations.**

**Related Calculators: **

**HCF Calculator:** Finding the Highest Common Factor is similar to the Greatest common factor or divisor as HCF is also known as GCF or GCD. You can calculate HCF of given numbers easily by approaching the standard methods manually. If you want to make your calculation of the Highest common factor effortlessly & quickly then using the HCF Calculator is the best option. By just taking the given inputs, the HCF Calculator provides the largest integer in a split second. Also, it gives detailed procedures along with show work.

The largest common factor that divides the given set of numbers exactly with zero remainders is known as the Highest Common Factor(HCF). HCF also is known as GCF and GCD. For two integers ie., a, b the HCF is indicated as HCF(a,b).

For example, if you take two numbers ie., 54 and 60 then the Highest Common Factor of numbers is the 6 ie., the largest integer that exactly divided the two numbers with zero remainders. Therefore, **HCF(54, 60) is 6**.

**Procedure to Find the Highest Common Factor of Given Numbers**

For a better understanding of the HCF of numbers, we are giving manual procedures on how to calculate the HCF of given numbers with different methods. There are so many methods to find out the Highest common factor of numbers but major methods that everyone should be aware of are providing here in a detailed way. They are as follows:

- List of Factors Method (Factoring)
- Prime Factorization Method
- Division Method
- HCF Using Euclid’s Algorithm

**HCF of Given Numbers By Factoring**

By using the Factoring method, we can easily find the HCF of numbers. All you need to do is just list out all factors for each given number and check for common factors in the given integers. Thereafter, consider the largest common factor from the list of common factors you found as the Highest Common factor of given numbers.

Look detailed steps of finding the HCF of Numbers using a list of factors method from the below given solved example and understand the method efficiently.

**Example:**

Find the HCF of 60 and 40 using the factoring method?

**Solution:**

Given number are 60 and 40

Now, we are finding the HCF(60, 40) by factoring

At the First Step, you need to list out the factors of 60 and 40

**Factors of 60**

List of all factors of 60 that divides with zero remainder are 1,2,3,4,5,6,10,12,15,20,30,60

**Factors of 40**

List of all factors of 40 that divides with zero remainder are 1,2,4,5,8,10,20,40

At the Second Step, need to separate the common factors from the given number factors list and find the largest integer

1, 2, 4, 5, 10, **20**.

The bolded number is the largest common factor of both integers so it can be considered as the highest common factor of 60 and 40.

Therefore, **HCF of 60 & 40** is **20**.

If your given numbers are big to solve then prime factorization is the best method compared to factoring. So, check out the steps to calculate the HCF of given numbers by prime factorization here:

- In this method, first and foremost, you need to list out the prime factors of each given integer.
- Then, separate the common prime factors of each number and make a list of the common prime factors.
- Also, comprise the highest number of occurrences of each prime factor ie., common to each given number.
- Finally, multiple these common prime factors to attain the Highest Common Factor of Given Numbers.

Let's check the closer look of finding the HCF of numbers by Prime factorization with the help of show work given below.

**Example:**

Find the Highest common factor of 40 and 60 by prime factorization?

**Solution:**

Given numbers are 40 and 60,

Now, we have to find HCF(40, 60) using Prime factorization

**Step 1:** Find the prime factors for 40 and 60,

The prime factorization of 40 is 2 x 5.

The prime factorization of 60 is 2 x 3 x 5.

**Step 2:** List out the highest number of common prime factors of 40 and 60 ie.,

2 x 2 x 5

**Step 3:** Now, on multiplying the common prime factors we will get the HCF of two numbers

2 * 2 * 5 = 40

Thus, the Highest Common Factor of 40 and 60 is **20**.

**Highest Common Factor of Numbers by Division Method**

The procedure to find the HCF of number by division method is as follows:

- First, consider the given numbers and find which is large and small then divide the large number by small number.
- In the second step, the divisor becomes the new dividend, now divide the dividend number by divisor.
- Repeat the same process until you get the remainder zero, then the last divisor is considered as the HCF of two numbers.

**Example:**

Find the HCF of 30 and 42 using the Division method?

**Solution:**

Given numbers are 30 and 42

For finding the HCF of given numbers by division method, you need to take a large number i.e., 42 as dividend and a small number ie., 30 as a divisor.

Now, divide 42 by 30 and get the HCF of 30 and 42 by performing the division method.

When you get the remainder zero then that divisor i.e., 6 is the HCF of given numbers.

Thus, HCF of 30 and 42 is **6**.

If you want to explore more about the HCF, GCF, LCM, Prime Factorization, etc. then visit lcmgcf.com and learn all these concepts clearly.

**1. What does HCF Stand for? **

HCF stands for Highest Common Factor also known as GCF & GCD as well.

**2. What is meant by HCF of Numbers?**

The highest number that exactly divides the given numbers with Zero Remainder is called the Highest Common Factor (HCF).

**3. How many methods are there to calculate the Highest Common Factor(HCF)?**

To calculate the HCF of Numbers, students can use many methods like:

- Factorization
- Prime Factorization
- Division Method
- Euclid's division lemma and many other

**4. How do you solve the Highest Common Factor of Numbers using a calculator?**

All you need to perform is just enter the given values in the input box of the HCF Calculator and then hit on the Calculate button to attain the result of HCF of numbers in a fraction of seconds.