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# Handling the Greatest Common Factor

Posted: Oct 15, 2017

We do mathematics in virtually all the aspects of life. When we are walking its mathematics when take shower it is mathematics when we talk it is mathematics finally when we do businesses its mathematics. You can never avoid mathematics, but you will find yourself at least calculating something. There is something known as the greatest common factor in mathematics. Have you ever come across it? Do you understand in simple terms what it means? This term usually abbreviated as GCF is that largest number that divides all the numbers given in a sequence without any remainder. For example, 12, 18, 24 the GFC is 6.

In the solution of GFC, have to identify the prime factors of each of the given numbers. After identification of the prime factors of each of the numbers, next thing to do is identifying the common prime factors that the numbers are given a share in common. For example,

Find the common factors for 30and 60. We shall start by listing down all the prime factors of each of the numbers. I.e. 30 = 2, 3, 5

60= 2, 3, 5

When all these common factors are multiplied, their product equals to 30. Therefore the greatest common factor is 30.

When solving the GFC of variables, the first thing to do is factoring the numbers. You have to identify and list all the numbers that the variables share in common. You can as well factorize the numbers and come up with a common factor. This is applicable only if you are provided with the numbers and the variables. Examples,

Workout the greatest common factor of 4x and 8xy, the answer becomes 4x.

Workout the greatest common factor of 3x^2y and 5x^2y^2 the answer is x^2y. These are examples of variables which you may meet in an examination, and you may be required to work out their GCF.

After looking at the GCF, the common question that may ring into the minds of readers is what is LCM? And what is the difference between LCM and GCF? Well, LCM is an abbreviation for the least common multiple; this is the smallest numbers that multiply a given number, for instance. The LCM of 8 is 2, 4 and 8. These numbers when multiplied by at least one of them in the pair the answer becomes 8. 2 and 4 can be referred to as the common factors of 8.

The major difference between GCF and LCM is that GCD works on division, ie that number that evenly divides two numbers whereas LCM relies on that number shared between two numbers. In occasions when the numbers only share 1 and themselves as the common factors then such numbers can never be related to each other. Therefore, both GCF and LCM tries to identify and look at how numbers relate to each other in terms of other numbers.

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