Greatest Common Factor of 84 and 138
GCF(84, 138) = 6, Greatest common factor of 84 and 138 is 6. Greatest Common Factor or Greatest Common Divisor of two numbers is the largest integer by which both the numbers can be divided. There are two different methods to calculate Greatest Common Factor of 84 and 138. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 84 and 138 by prime factorization method
We will first find the prime factorization of 84 and 138.
Prime Factorization of 84 is 1, 2, 2, 3, 7 and Prime Factorization of 138 is 1, 2, 3, 23.
- Factorize\( (84) = \) \(1\times 2\times 2\times 3\times 7\)
- Factorize\( (138) = \) \(1\times 2\times 3\times 23\)
Now we need to find any which are common for each number (1, 2, 3) and multiply these numbers together.
\(GCF(84, 138) = 1\times 2\times 3 = 6\).
Greatest Common Factor of 84 and 138 by matching factors method
List of positive integers factors of 84 leaving a remainder zero is 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
List of positive integers factors of 138 leaving a remainder zero is 1, 2, 3, 6, 23, 46, 69, 138
As you can see, 6 is the greatest and common number that 84 and 138 divides into.
So the greatest common factor 84 and 138 is 6.
\(GCF(84, 138) = 6\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
