Greatest Common Factor of 120 and 9728
GCF(120, 9728) = 8, Greatest common factor of 120 and 9728 is 8. 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 120 and 9728. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 120 and 9728 by prime factorization method
We will first find the prime factorization of 120 and 9728.
Prime Factorization of 120 is 1, 2, 2, 2, 3, 5 and Prime Factorization of 9728 is 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 19.
- Factorize\( (120) = \) \(1\times 2\times 2\times 2\times 3\times 5\)
- Factorize\( (9728) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 19\)
Now we need to find any which are common for each number (1, 2, 2, 2) and multiply these numbers together.
\(GCF(120, 9728) = 1\times 2\times 2\times 2 = 8\).
Greatest Common Factor of 120 and 9728 by matching factors method
List of positive integers factors of 120 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
List of positive integers factors of 9728 leaving a remainder zero is 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1216, 2432, 4864, 9728
As you can see, 8 is the greatest and common number that 120 and 9728 divides into.
So the greatest common factor 120 and 9728 is 8.
\(GCF(120, 9728) = 8\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
