Greatest Common Factor of 200 and 345
GCF(200, 345) = 5, Greatest common factor of 200 and 345 is 5. 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 200 and 345. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 200 and 345 by prime factorization method
We will first find the prime factorization of 200 and 345.
Prime Factorization of 200 is 1, 2, 2, 2, 5, 5 and Prime Factorization of 345 is 1, 3, 5, 23.
- Factorize\( (200) = \) \(1\times 2\times 2\times 2\times 5\times 5\)
- Factorize\( (345) = \) \(1\times 3\times 5\times 23\)
Now we need to find any which are common for each number (1, 5) and multiply these numbers together.
\(GCF(200, 345) = 1\times 5 = 5\).
Greatest Common Factor of 200 and 345 by matching factors method
List of positive integers factors of 200 leaving a remainder zero is 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
List of positive integers factors of 345 leaving a remainder zero is 1, 3, 5, 15, 23, 69, 115, 345
As you can see, 5 is the greatest and common number that 200 and 345 divides into.
So the greatest common factor 200 and 345 is 5.
\(GCF(200, 345) = 5\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
