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## What is the meaning of HCF?

Before we begin with the calculations part of HCF, let us be clear of the fact that this HCF or the highest common factor is the other word for GCD or the greatest common divisor or GCF / greatest common factor or highest common divisor or GCM / greatest common measure. And as far this GCD is concerned then in mathematics, it turns out to be the greatest common divisor of either 2 or more than that integers only when at the least one of them does not happen to be a 0. It is also stated to be the largest positive integer which divides numbers without leaving a reminder.

## HCF Calculator

\(E.g.\, GCD \, of \, 8\, and \ 12\,=\,4\)

## How to find GCD / HCF of a number?

Let us take the example of 54 to understand as to how GCD is calculated. Moreover, this number 54 can also be expressed in the form of 2 integers that too in quite some number of ways in the following manner –

\(54 \, \times\, 1\,=\,27\, \times \,2\,=\,18\, \times \, 3\,=\,9\times 6\)

Hence the divisors of 54 are as follows -\( 1,2,3,6,9,18,27,54\)

On the other hand, divisors of 24 have been mentioned here -\(1,2,3,4,6,8,12,24.\)

\(common \, divisors\, of\, 54\, and\, 24\,=\,1,2,3,6. \)

\(greatest \, common\, divisor\, of\, 54\, and\, 24\, is \,6 \)

\(gcd(54,24)=6 \)

Hence, in the above manner, one will be able to write the GCD of a given number.

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## How to calculate HCF?

One can make use of the prime factorization method in order to calculate HCF / GCD. To get to know as to how to calculate this HCF, we have taken 2 numbers which are 48 & 180 respectively & given below are the prime factorizations of these 2 numbers.

\(48\, =\,2 \times 2 \times 2 \times 2 \times 3 \)

\(180 \,= \,2 \times 2 \times 3 \times 3 \times 5\)

In the equation given above, the common number shared by 180 & 48 is nothing but 2 & 3.

\(therefore,Greatest \,common\, divisor\, = \,2 \times 2 \times 3\, =\, 12\)

An individual will have to keep the simple fact in mind that though there are a number of methods to calculate the greatest common divisor or the highest common factor, still the most – commonly used method to know this GCD is prime factorization method.

### Formula for HCF

There is another formula to know the greatest common divisor or the HCF of a number & the formula which is put in to use has been given below –

\(H C F\,=\, \frac {H C F \,of\, numerators}{L C M \,of \,denominators}\)

## How to use an online HCF calculator?

To make use of the HCF calculator which is available on this site, the user will be required to follow the steps mentioned below. Firstly, the user will have to enter the number in the field provided & then click on the calculate tab. However, if you again wish to find the HCF or are not so sure about the numbers entered then click on reset tab to re – enter the numbers.