Greatest Common Factor of 1200 and 3200
GCF(1200, 3200) = 400, Greatest common factor of 1200 and 3200 is 400. 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 1200 and 3200. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 1200 and 3200 by prime factorization method
We will first find the prime factorization of 1200 and 3200.
Prime Factorization of 1200 is 1, 2, 2, 2, 2, 3, 5, 5 and Prime Factorization of 3200 is 1, 2, 2, 2, 2, 2, 2, 2, 5, 5.
- Factorize\( (1200) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 5\times 5\)
- Factorize\( (3200) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 5\times 5\)
Now we need to find any which are common for each number (1, 2, 2, 2, 2, 5, 5) and multiply these numbers together.
\(GCF(1200, 3200) = 1\times 2\times 2\times 2\times 2\times 5\times 5 = 400\).
Greatest Common Factor of 1200 and 3200 by matching factors method
List of positive integers factors of 1200 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200
List of positive integers factors of 3200 leaving a remainder zero is 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200
As you can see, 400 is the greatest and common number that 1200 and 3200 divides into.
So the greatest common factor 1200 and 3200 is 400.
\(GCF(1200, 3200) = 400\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
