What is GCF? How to find the GCF of two numbers?

A factor is a number that, when multiplied by other numbers, produces the desired results. Factors is the name given to the resulting number. The numbers can usually be factored into various combinations. If you know your multiplication tables, you can easily work out the variables. Here, we’ll look at what the biggest common factor is and how to find the GCF of two given numbers on a number line.

What if GCF?

The Greatest Common Factor is the largest number that is a factor of two or more numbers (GCF). The greatest number (factor) divides them, yielding a Natural number. Once all of the number variables have been discovered, there are a few that are shared by both. The greatest common factor is the number that appears most often in the common factors. The GCF is also named as the Highest Common Factor of a number. Let us see an example of GCF – The GCF of 18, 21 in a number set is 3. This is because the factors of the number 18 and 21 are given below:

  • Factors of the set 18 = 2 × 9 = 2 × 3 × 3
  • Factors of the set 21 = 3 × 7

Here, the number 3 is common in both the factors of numbers given in the set above. Therefore, the greatest common factor of numbers 18 and 21 in the set is 3.

How to Find the GCF of two numbers?

If one has to find out or know the GCF of two numbers in a number set, they will initially have to list all the existing prime factors of each given number. The multiple common factors of both the numbers in the last stage give us the GCF. If there are no present common prime factors, the greatest common factor is invariably 1.

Finding the GCF of a given number set can be very manageable. However, there are several steps that need to be followed to get an accurate and precise GCF. In order to find the greatest common factor of two given numbers in a number set, one needs to list down all the factors of both the numbers and then identify the highest common factor. Let us consider this example of finding the GCF of 18 and 24

  • Lets first list down the Prime factors of 18 – 2×3×3
  • Then the Prime factors of 24 –2×2×2×3

Now, we have factors 2 and 3 in common so, consequently, G.C.F of 18 and 24 is 2×3 that gives us 6 as the final answer.

How to Find the Greatest Common Factor(HCF)?

Following are 3 primary methods for finding the greatest common factor of two numbers given in a number set.

Listing Out Common Factors

This approach allows you to list the common factors of both numbers, making it simple to search for them. We can choose the best one among all of them by labeling the common factors.

Prime Factorization

Starting with the smallest prime factor, prime factorization is a method of expressing a number as a function of its prime factors.

Division Method

Long division is a method of breaking down a division problem into a series of simpler steps, while division is a method of grouping items in equal classes. The largest positive integer that divides equally into all the given numbers without leaving any remainder is the greatest common factor (GCF) of a set of whole numbers.

Finding out the HCF of Multiple Numbers

Math experts have spoken about how to find the GCF of two numbers. What if there are more than two numbers in the equation? When there are a lot of numbers, it’s difficult to come up with a list of common factors. As a result, we can use one of the following methods: Long Division or Prime Factorization.

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