Greatest Common Factor –Different Ways to Find GCF
When we talk about the easiest topic in math, then GCF will be the first name came from the mouth of students. The greatest common factor is a number which is common in two different numbers. In other words, two numbers have been taken and then their factors are compared with each other to know about the GCF. Besides this, there are different ways to solve it so let’s know about them.
Comparing Common Factors
I know many of you heard about the prime factorization method, but there is an alternative method for this. Here are the steps for it:
• At first, take tow numbers for example 30 and 25. Now, start finding their factors. 1, 2, 3, 5 and 30 are the factors of 30. Now, the factors of 25 are 1, 5, 25 and 5.
• Now, in the second step, we will be comparing both the numbers factors and find out the common numbers which are 1 and 5. But there are two numbers are common in it, and thus we choose the biggest common number which is 5.
• So, the greatest common factor of 30 and 25 is 5.
Using prime numbers
Now, let’s move on to the prime numbers as they are a bit of complicated as there are various conditions which need to apply in it.
1. Find the prime factors
For finding out the prime factor, you need to find the numbers that product will be equal to the number itself. For better understanding, let’s look at an example:
• Factors of 35 are 1, 5, 7 and 35.
• Factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
Now, we have to find the prime factors of it which are 5 and 7 of 35 and 2, 3 and 7 of 42. When all the numbers have been multiplied then the result obtained from it are 35 and 42.
2. Find common numbers from the prime factors
In the second step, you have to compare the obtained prime factors. For example, prime factors of 30 are 5 and 7. Taking about the prime factors of 42 then they are 2, 3 and 7. So, when you finished comparing then, you will find out that there is only one number which is common in both the prime factors. Besides this, that common number is seven, and thus the greatest common factor of 30 and 25 is 7.
Well, there is another case in it as when one will get more than one common prime factor when two numbers are compared. In that case, you have top gathered all the common numbers together and then choose the number which is common in both the list. After that, multiply the common numbers and you will get the GCF from it.
Well, make sure that you the factors you find will be right otherwise it will lead to the wrong answer. So, use these easy methods as they are super easy and be the master of Greatest Common factor.