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Find The Greatest Common Factor

Are you looking for a process to find the greatest common factor of two, three, four number, or set of numbers? It is very easy to find the GCF of a set of numbers but you need to follow some steps to find the greatest common factor. First of all, you need to know what is the greatest common factor? According to the name of the factor is the greatest common factor. It means to maximize the common number which is available in all factors of the number.  There are two ways to find the greatest common factor number first you find the GCF from a prime number and other to find the factor and assume which one is the greatest number in the series of any number of factors.  I will explain both ways to find GCF or any number. Let’s start through one example:

Example1: Greatest Common Factor of 24 and 30

Method 1. Find the GCF through factorization.

Factors of 24 = 1, 2, 3, 4, 6, 8 12 and 24

Factors of 30 = 1, 2, 3, 5, 6, 10, 15, and 30

Common factor of 24 and 30 is 1, 2, 3, and 6

The greatest common factor of 24 and 30 is 6.

Method 2. Find the GCF through Prime Factor.

find Prime factors of 24.

\(
\begin{array}{c|lcr}
2 & \text{24} \\
\hline
2 & 12 \\
\hline
2 & 6 \\
\hline
3 & 3 \\
\hline
1 & 1 \\
\end{array}
\)

find Prime factors of 30.

\(
\begin{array}{c|lcr}
2 & \text{30} \\
\hline
3 & 15 \\
\hline
5 & 5 \\
\hline
1 & 1 \\
\end{array}
\)

Prime Factor of 24 = 2, 2, 2, and 3

Prime factor of 30 = 2, 3, and 5

Common prime factors = 2, 3

Greatest Common factors of 24 and 30 is 2 X 3 = 6

Example2: Greatest Common Factor of 18 and 28

Method 1. Find the GCF through factorization.

Factors of 18 = 1, 2, 3, 6, 9, and 18

Factors of 28 = 1, 2, 4, 7, 14, and 28

Common factor of 18 and 28 is 1, and 2

GCF of 18 and 28 is 2.

Method 2. Find the GCF through Prime Factor.

find Prime factors of 18.

\(
\begin{array}{c|lcr}
2 & \text{18} \\
\hline
3 & 9 \\
\hline
3 & 3 \\
\hline
1 & 1 \\
\end{array}
\)

find Prime factors of 28.

\(
\begin{array}{c|lcr}
2 & \text{28} \\
\hline
2 & 14 \\
\hline
7 & 7 \\
\hline
1 & 1 \\
\end{array}
\)

Prime Factors of 18 is 2, 3, 3, and 1

Prime factor of 28 is 2, 2, 7, and 1

Common Prime Factor of 18 and 28 is 1 and 2

GCF of 18 and 28 is 1 X 2 = 2

We have shared the greatest common factor techniques to easily find the GCF or any set of numbers. If you have any doubts or issues regarding these methods please let me know through social media and mail.

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