Greatest Common Factor of 204 and 102
GCF(204, 102) = 102, Greatest common factor of 204 and 102 is 102. 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 204 and 102. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 204 and 102 by prime factorization method
We will first find the prime factorization of 204 and 102.
Prime Factorization of 204 is 1, 2, 2, 3, 17 and Prime Factorization of 102 is 1, 2, 3, 17.
- Factorize\( (204) = \) \(1\times 2\times 2\times 3\times 17\)
- Factorize\( (102) = \) \(1\times 2\times 3\times 17\)
Now we need to find any which are common for each number (1, 2, 3, 17) and multiply these numbers together.
\(GCF(204, 102) = 1\times 2\times 3\times 17 = 102\).
Greatest Common Factor of 204 and 102 by matching factors method
List of positive integers factors of 204 leaving a remainder zero is 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
List of positive integers factors of 102 leaving a remainder zero is 1, 2, 3, 6, 17, 34, 51, 102
As you can see, 102 is the greatest and common number that 204 and 102 divides into.
So the greatest common factor 204 and 102 is 102.
\(GCF(204, 102) = 102\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
