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