HCF Calculator

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.

What is Factoring?

Factoring also called "Factorising" at several places is the procedure of finding the factors. In other words, Factoring is Discovering what to multiply together to get an expression. Moreover, It is like "splitting" an expression into a multiplication of simpler expressions.

What is the Difference Between HCF and LCM?

HCF and LCM are two completely different phrases in mathematics. The full form of LCM is Lowest Common Multiple or Least common multiple but HCF is the abbreviated term for Highest Common Factor.

The H.C.F comprehends the greatest or highest factor that is existing in between given two or more sets of numbers whereas L.C.M interprets the least or lowest number which is exactly divisible by two or more sets of numbers or is its exact divisor. Furthermore, the HCF of any given set of numbers can not be bigger than any of them whereas the LCM of a given set of numbers can not be smaller than them.

Additionally, H.C.F is also recognized as the greatest common factor (GCF) whereas LCM is also known as the Least Common Divisor.

How to Calculate HCF without Using a Calculator?

We can find HCF easily by Prime Factorization without using a calculator or by directly calculating with its formula.

For finding HCF by prime factorization,

1. Firstly, in order to find the HCF of the given numbers by prime factorization, we find the prime factors of those numbers. 
2. After getting the factors, 

Multiply all the prime factors that are common to each of the given numbers to get a product.

1. Finally, the product is the HCF of the given set of numbers.

For finding HCF by formula, 

The HCF formula for two different numbers 'a' and 'b' is formulated as 

HCF (a, b) × LCM (a, b) = a × b.

In other words, the formula states that the product of any two numbers is equal to the product of their HCF and LCM. 

1. Put the values correctly in the formula.
2. Evaluate it.

Tricks for calculating HCF 

• If 1 is the Highest Common Factor or HCF of any two numbers, then their LCM will be their product. For example, the HCF of 2 and 5 is 1, now the LCM of 2 and 5 will be 2 × 5 = 10.
• For any two coprime numbers, the Highest Common Factor or HCF is always 1. For example, if we take two co-prime numbers 4 and 5, we can see that their HCF is 1 because co-prime numbers do not have any mutual factor other than 1.

Solved Example HCF Calculation With Steps

Example:

 Find the HCF of 50 and 75 by the prime factorization method.

Solution:

Firstly, Let us list all the prime factors of the given set of numbers. 

The prime factors of 50 are 2 × 5 × 5

The prime factors of 75 are 3 × 5 × 5

As we can see, The common factors of 50 and 75 are 5 × 5 and the factors occurring in 50 and 75 both are 5 × 5. 

Therefore, HCF of (50, 75) = 25.

Visit hcflcm.com to find solutions to your problems and understand tough mathematical concepts.

FAQs on Free Online HCF Calculator with Steps

• Why do we calculate HCF?

HCF is required in determining the greatest factor that is shared by two or more numbers.

• What is HCF and LCM example?

Let's take an example of 18 and 42, 

The least common multiple for 18 and 42 is 126 while 6 is the highest common factor for the two numbers.

• What is the HCF of 2923 and 3239?

79 is the highest among the common factors shared by the two numbers 2923 and 3239, hence, HCF= 79

• What is the fastest way to find the HCF?

The fastest way to determine the HCF of two numbers is to multiply all the factors present in the factor list of the two numbers.