Top 5 Easy Methods To Find The Highest Common Factor HCF

The complete H.C.F. representation is the Highest Common Factor. It is the common factor among two possible values provided and it is also termed the Greatest Common Factor (GCF).

The other terms that are used for H.C.F. are

• Greatest common factor (GCF)
• The greatest common denominator (GCD)
• Highest common factor (HCF)
• Greatest common divisor (GCD)

We used to employ two key approaches to find H.C.F, prime fractionation, and division method. Both these methods are easy and all of us have learned in our earlier classes. A method of division is the shortcut and basic method for finding both H.C.F.

In this article, we’ll enlighten some easiest methods that you can use to find H.C.F. and we will also solve some problems that are based on these concepts to make you understand better.

When we define the term H.C.F. as dictated by the rules of arithmetic, the largest common divisor, or the GCD of two or more positive integers, usually occurs to become the largest positive integer dividing the figures without leaving any remainder.

For example

Take the 16 and the 20 for instance. The 16 and 20 have H.C.F.4 because this is the highest number capable of dividing 8 and 12.

There are indeed a lot of different ways to obtain the greatest or highest common number factor. The most effective approach you employ depends on how many numbers you have, how large they are, and what you are going to do with the outcome.

Factoring method

Identifying all of the factors of each number is a significant step to figure the HCF by factoring and for more simplicity, you can find them with a Factors Calculator. Factors of the whole number are numbers that divide equally into the number with zero remaining. The HCF is the largest number common to each list, given the list of common factors for each number. This method is also known as prime factorization.

For example:

What is the HCF of 18 and 36

The number 18 has 6 factors that are 1, 2, 3, 6, 9, 18.

The number 36 has 8 factors that are 1, 2, 3, 4, 6, 9, 12, 36.

Thus, the common factors of 18 and 36 are clear 1, 2, 3, 6, and 9.

Thus, it is clear that the greatest common factor of 18 and 36 is 9.

Finding prime factors

Finding a prime number is a simple method because primary factors are defined as the factors of a number which are the prime numbers themselves. There are many methods of finding a number’s prime factors, but one of the most common is using a tree of prime factors.

Or there is a simple method that can be used to find the prime factors is to get the number by combining the common ones:

For example

Two numbers are 24 and 108

The prime factors for 24 are 2 × 2 × 2 × 3 = 24

The prime factors for 108 are 2 × 2 × 3 × 3 × 3 = 108

You can observe that the greatest common factor among both are 2 × 2 × 3 = 12

Thus HCF = 12

Play around method

This is another method you can use to find the highest common factor. It is the most basic method that is used to clear the HCF concept of school kids.

It works with just playing around the numbers until you get the factor.

For example

Two numbers are 9 and 12

3 × 3 = 9 and 3 × 4 = 12

Thus, the highest common factor, in this case, is 3.

Division method

You need to take two of the given numbers for finding HCF by this method. Start by dividing the larger by the smaller and then divide the divisor by the remainder. Now divide the divisor of this division again by the next remaining that has been found and repeat this method until the remainder becomes zero.

The last divisor found is the HCF of the two numbers that are being asked. If three numbers are given and you need to find the three-number HCF then find the two-number HCF and the third number.

What will be the HCF of 327 and 436?

 Here first you have to identify one smaller number. And this small number is taken as a divisor to divide the larger number. For example, in this case, 327 is a smaller number than the 436 that is a larger number. So, you will divide 327 by 436.

Here the remainder is 109. Now327 is divided by 109.

So, the HCF of 327 and 436 is 109.

Euclid’s Algorithm

In case when you have to find HCF of very large numbers like 182664, 154875, and 137688, Euclid’s algorithm is used.

How to Find the HCF Algorithm Using Euclid

• Subtract the smaller number from the larger number given two whole numbers and note the result.
• The above process is repeated by subtracting the smaller number from the result until the result is smaller than the smaller number initially.
• Using the small number initial as the bigger number new. Subtract the result from the new bigger number from phase 2.

HCF calculator

HCF Calculator is simply an online tool that anyone can use to find HCF problems more quickly. There are numerous calculators available all over the internet for example Meracalculator is a website that provides you with the HCF calculator. Of course, it can save you from tedious computations and algebraic manipulations.

The calculator that can find HCF is also referred to as the HCF finder. The great thing about the calculator is that it will determine the greatest common factor of a set of two to N numbers in a fraction of time. Among the methods we have mentioned earlier to find HCF, the easiest and quick method to calculate HCF is by using an online calculator.

How to use HCF calculator

After finding any suitable website of a calculator, just enter the numbers with comma separation that you want to find HCF.

These calculators will show your input expression in a box, then you need to select the method of finding HCF. If it is exactly the same that you want then, click the ‘go’ button.

The results will be on your screen.

Although, these HCF calculators support all the methods such as the prime fractioning method, division method, and Euclid’s algorithm method, etc.