Greatest Common Factor of 240 and 204
GCF(240, 204) = 12, Greatest common factor of 240 and 204 is 12. 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 240 and 204. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 240 and 204 by prime factorization method
We will first find the prime factorization of 240 and 204.
Prime Factorization of 240 is 1, 2, 2, 2, 2, 3, 5 and Prime Factorization of 204 is 1, 2, 2, 3, 17.
- Factorize\( (240) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 5\)
- Factorize\( (204) = \) \(1\times 2\times 2\times 3\times 17\)
Now we need to find any which are common for each number (1, 2, 2, 3) and multiply these numbers together.
\(GCF(240, 204) = 1\times 2\times 2\times 3 = 12\).
Greatest Common Factor of 240 and 204 by matching factors method
List of positive integers factors of 240 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
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, 12 is the greatest and common number that 240 and 204 divides into.
So the greatest common factor 240 and 204 is 12.
\(GCF(240, 204) = 12\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
