In basic arithmetic, in processes that involve both multiplication and division, HCF plays a very important role. Let us take a closer look at the principles on which the whole HCF ideas were based.
What is HCF?
The highest or largest factor common to any two or more natural numbers given is referred to as the HCF of the that provided numbers. There are a couple of other terms that are also used for representing HCF are GCD (Greatest Common Divisor), the greatest common denominator (GCD), and the greatest common divisor (GCD) as well.
Getting some knowledge of factors and multiples can be helpful to identify HCF (Highest Common Factor) and LCM (Least Common Multiple).
What are the factors and multiples?
When you talk about any number factor, we’re referring to any number that absolutely divides that given number, with no remainder. The reasons for 27, for example, are 1, 3, 9, and 27 alone. The number 4 cannot divide the number 10 without a remainder. If we divide when you divide the number10 by 4, the answer is obviously 2.5 that does not fall under the integer numbers. For this reason, 4 cannot be defined as a factor of 10. We must note that the variables are either less than the original number or equal to it.
On the other hand, you were actually practicing multiples when you talked about multiples. When you learned your counting tables in primary school such as 2, 4, 6, 8, and 10, 12, they are all multiples of 2. You have multiplied 2 by 1, 2, 3, 4, and 5, which are integers, in order for us to get these numbers.
How to find HCF?
Now that you have learned knowledge about what are multiples and variables, we are going to move towards the formal concept of HCF and understand it even better.
Finding the Highest Common Factors of the numbers is an easy and easy method. Generally, there are two primary methods that everyone finds easy to determine the HCF (Highest Common Factor) of the numbers. They are the Prime Factorization Method and Division Method.
It is a simple method to determine the highest common factor. This factorization method involves transcribing the two or more numbers of all of the variables/divisors involved. The thing to be the focus is to keep in mind the largest or the highest number when you are listing the divisors of a certain number, which generally divides the numbers without leaving any remainder.
Q.1) Find out the HCF of 16 and 32 using the factorization method.
Factors of number 16 are known to be 1, 2, 3, 4, 6, 8, and 16 itself.
(1 × 16, 2 × 8, 3 × 6, 4 × 4)
We know that the factors of 32 are 1, 2, 4, 6, 8, 16, and 32itself. (1 × 32, 2 × 16, 4× 8, 8x 8)
Thus, it is clear that the highest or the greatest factor in respect to the value of both the number 16 as well as 32 is 8, so, HCF of 16 and 32 becomes 8.
Prime factorization method:
It is another and important and easy strategy that involves two or more numbers that are taken as products of prime factors. We further specify the primary variables that are similar to the numbers discussed. The outcome of this method is mostly the common prime variable, which is indeed the Highest Common Factor or Greatest Common Divisor of the numbers.
Q.2) Find the HCF of 16 and 32, using the prime factorization method.
Solution: This method proceeds when we first find out the prime factors individually.
Prime factors of 16 are 2 x 2 x 2 x 2
Prime factors of 2 x 2 x 3 x 3
Thus, the HCF of 16 and 32 by prime factorization is 2 x 2 = 4
The division method of finding or calculating the HCF is another fine option. It works in those cases when you have to find out the HCF of the two of the given numbers.
In those two specific numbers, you must identify the greater and the smaller numbers. After that, start dividing the greater number to smaller ones and then divide the divider by the reminder. And this is the general method of executing the division method until you get the remainder zero.
When you talk about different methods for calculating HCF, you must not neglect there are several other ways for finding out the greatest or highest common number factor as well. Other than the above manual methods, the most reliable, quick, and easy to use the approach you can take advantage of is using an online calculator.
The GCF Calculator is basically an internet service that can be used by anyone to find HCF issues faster. As there are a lot of calculators across the internet that offers their completely free services, one of the famous one is meracalculator website that provides students with the HCF calculator to solve mathematical problems. It is, no doubt one of the top efficient and useful calculators of the website. Of course, it will save you from boring computations and manipulations of algebraic type.
Often known as the HCF-finder or calculator that can identify HCF in seconds. The great feature of the calculator is that in a fraction of time, it will calculate the greatest common factor of a list of numbers from two to infinite. Among the methods we listed earlier to find HCF, using an online calculator is the simplest and quickest way to calculate HCF.
How to use the HCF calculator? A step by step guide
- Once you have found the meracalculator website, open up the HCF calculator.
- Now you will input all of the numbers that you need to find HCF along with the comma separation.
- After putting the number, the calculator will show your input figures in its input field.
- Next, you must select the method of finding HCF. This step is important but in case it is exactly the same that you want then you would go to click the ‘calculate’ button.
- The outcomes will be on your display in a matter of seconds.
Plus, the point of the HCF calculator is that it supports all the methods such as the prime fractioning method, division method, and Euclid’s algorithm method, etc.