No person can imagine their life without understanding the basic concepts that are being taught right from the start of school. What if the person does not know numbers, the concepts related to them? This might be a sign of the problem for the people to see different things around them in life. This the reason, it is very important to know about the basic concepts of mathematics as they are very beneficial in life. You all might have come across the concept of HCF and LCM. But there is one more concept i.e. GCF known to be the greatest of all three.
GCF stands for Greatest Common Factor, it can be calculated of two or more integers that can be either positive or negative. This concept is known by different names like Highest Common Divisor, Higher Common factor, and even Greatest common divisor. The GCF of two or more numbers is the greatest number that is common among the factors of the given numbers. Let’s take the example of two numbers i.e. 24 and 30. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 14. On the other hand, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Here the greatest common factor among them is the number 6. So the result of the GCF among 24 and 30 is the number 6. This is also the greatest common divisor of these two numbers. To find the GCF, the person can use the factors of a number to easily calculate it. So, in nutshell is very important to understand this concept and get a better understanding of the different things around you. The expert teachers at Cuemath can offer more insight into the concept.
Here is a list of the secrets about the GCF. Let’s have a look at them.
- To calculate this, the person can follow 3 different methods and these are stated below:
- GCF by listing out the common factors: In this method, the common factors of the given numbers are calculated. Out of the list of the common factors, the highest number is selected to answer the GCF.
- GCF by Prime Factorization: Even it is very simple to calculate GCF through prime factorization as it will provide all the prime factors. The product of all the prime factors can give the GCF. For example, we take two numbers 24 and 30, in this 2 will divide both these numbers to give 12 and 15, and after this 3 is divide and it gives 4 and 5. Now there is no other common factor that will divide 4 and 5. So the product of the two prime numbers i.e. 2 and 3 is 6 and it becomes the GCF of 24 and 30.
- GCF by Division method: In this method, the grouping of the objects is done in equal parts. In case of the large numbers, a long division process is undertaken so that the following steps can be broken down into easier parts.
- Even it is possible to calculate the GCF of the multiple numbers at the same time. For this, mostly the prime factorization method and long division method are used to find the GCF.
- There is a huge difference between GCF and LCM as the name states that GCF is Greatest Common Factor and LCM Least Common Multiple. Both are used in different ways to give different answers.
- GCF is commonly used whenever it comes to fractions as we all use a lot of fractions every day from shopping to time calculation fractions are everywhere.
- In case the person wants to simplify the fraction, it can use the GCF and can divide them with the GCF number to make the calculation more fast and accurate.
- GCF is used in almost every type of arrangement done around us whether it is in rows, columns, distributing things among the people, etc. For these things, the person needs to have a better understanding of it.