What you need to do to find the greatest common factor

As the name suggests, the greatest common factor is the largest number that basically happens to be a common factor of two numbers (or more). Finding the greatest common factor is not hard at all. However, students who are starting out to find the greatest common factor for the first time might get a tad bit overwhelmed. But worry not, as with ample practice; it would become extremely easy to do so.

How to find greatest common factor

Now, the one thing that you need to know is that there are two different ways through which you can find greatest common factor. Here is a basic insight into them:

1. Using common factors to find GCF

The first method of finding the GCF of two or more number is that of comparing their common factors. What you basically need to do is find out all of the factors of the numbers that you have at hand. Consider this example:
example of finding greatest common factor

Now that you have found the factors of the two numbers, you need to compare them and then find the greatest numbers amidst them all.


find the greatest common factor

This is basically going to be the greatest common factor of the two numbers, which in this case is 1.

2. Making use of prime numbers to find the greatest common factor

When you make use of prime numbers in order to find the GCF of two numbers, you basically need to factor them completely into their prime numbers. What’s that? Well, a prime number is basically a number greater than 1 that does not have any factors apart from itself. For example, there’s 5, and 17 etc. Consider this example:


prime numbers in greatest common factor

Now that you have worked out the prime numbers, you need to pick the ones that are common amidst the two sets.

prime factors

Considering that there is just a single common prime factor, 7 is going to be the greatest common factor of 35 and 42. However, if there are more than one common prime factors, you basically need to multiply them in order to find the greatest common factor.

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