What is GCF(Greatest Common Factor)?

In Mathematics, the Greatest Common Factor or Greatest Common Divisor of numbers is the most important integer through which each integer may be divided.

For instance, in case you take the numbers 32, 256 the GCF of them might be 32 as it's miles the most important wide variety that divides precisely each of the given numbers.

GCF(32, 256) = 32

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How to locate the GCF of numbers?

There are some of the methods wherein you could locate the Greatest Common Factor. However, which approach might be suitable will in the main rely on the numbers you're having, how massive they're, and what you will do with the end result.

There are 3 predominant strategies through which you could locate the GCF of numbers and they're as follows

• Factoring
• Prime Factorization
• Euclid’s Algorithm

Let’s get deep into every of the approach by taking sufficient examples so you will recognize the idea of the Greatest Common Factor of numbers easily.

GCF of Two Numbers through Factoring Method

In order to locate the GCF of numbers the usage of Factoring listing out all elements of every wide variety. Whole wide variety elements are people who divide the wide variety frivolously leaving the rest 0. Once you understand the listing of not unusualplace elements GCF is the most important wide variety not unusualplace in every of the listing.

Example

Find the GCF of numbers 36 and forty-five?

Solution:

Given numbers are 36 and forty-five

List of Positive Integers for the wide variety 36 leaving the rest 0 is 1, 2, three, 4, 6, 9, 18, 36

List of Positive Integers for the wide variety forty-five leaving the rest 0 is 1, three, five, 9, 15, forty-five

Greatest Common Factor of (36, forty-five) this is biggest and not unusualplace in each the elements is 9.

Thus, GCF of 36, forty-five is 9.

GCF of Numbers through Prime Factorization Method

In order to locate the GCF of numbers the usage of the high factorization approach listing the high elements of every wide variety. List the Prime numbers which can be not unusualplace to every one of the numbers. Include the best wide variety of occurrences of every high wide variety not unusualplace to every authentic wide variety. Multiply them to get the Greatest Common Factor.

You will locate high factorization less difficult in comparison to the factoring approach whilst the numbers are massive.

Example

Find the GCF of numbers 15, forty-five the usage of the Prime Factorization Method?

Solution:

Prime factorization of 15 is three x five

Prime factorization of forty-five is three x three x five

The maximum wide variety of occurrences of every high wide variety not unusualplace to every authentic wide variety is three*five and on multiplying you may get the GCF as 15

GCF of (15,forty five) is 15