The GCF of two non-zero integers x and y is the greatest positive integer z, such that z is a divisor of both x and y. GCF stands for greatest common factor. The GCF of two numbers x and y is usually denoted by GCF(x,y). Other names given to GCF are the greatest common divisor (GCD) and highest common factor (HCF). The GCF can be a factor of two or more given numbers. When a factor is shared between two or more numbers, it is referred to as a common factor. The value of the factor which is the highest becomes the greatest common factor of those numbers. There are a number of ways that can be used to calculate the GCF of numbers; however, we will list out the two easiest methods with examples.
Methods to Calculate the GCF
1. Listing Method
The first method introduced to children for calculating the GCF of natural numbers is the listing method. We make a list of all the factors of the given numbers. Then we proceed to extract the common factors and make another list. The common factor with the highest value provides us with the GCF of the given numbers. Let us take a look at an example to get a better understanding of how to use this method.
Use the listing method to find the GCF of 8 and 10
- Factors of 8 = 1, 2, 4, 8
- Factors of 10 = 1, 2, 5, 10
- Common Factors = 1, 2
- As 2 has the greatest value among the common factors the GCF of 8 and 10 is 2.
2. Prime Factorization
The issue with the listing method is that it cannot be used for very large numbers. Suppose you have to find the GCF of 10098 and 78964, the list of factors will be never-ending. Additionally, if you have to find the GCF of more than two large numbers, the process will become very complicated. In such a case, you have to turn to the prime factorization method. In this method, the first step is to write all the given numbers in the form of the product of their prime factors. Next, we make a list of all the common prime factors. By multiplying them, we can get the GCF of the given numbers. Let us have a look at an example.
Find the GCF of 8 and 10 using the prime factorization method.
- Prime Factors of 10 = 2 * 5
- Common Factors = 2
- Thus, the GCF of 8 and 10 is 2
Irrespective of the method used, the GCF of two or more numbers will always be the same. You have to use your own acumen to decide which method to apply in case it is not specified in a question. The one thing to focus on while studying this topic is to make sure that you can break numbers down into their factors and prime factors quickly. If you can improve your speed and accuracy in doing calculations, you can master this topic in no time.
The GCF is used in several topics and problem sums. It is vital for your kids to get the proper guidance so that he does not fear the subject. Cuemath is an incredible educational platform that provides a well-structured curriculum to kids ensuring that they do not get confused while studying. The Cuemath tutors use several resources to deliver an impactful lecture. Thus, a kid can have fun while learning.