Greatest Common Factor of 120 and 7575
GCF(120, 7575) = 15, Greatest common factor of 120 and 7575 is 15. 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 7575. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 120 and 7575 by prime factorization method
We will first find the prime factorization of 120 and 7575.
Prime Factorization of 120 is 1, 2, 2, 2, 3, 5 and Prime Factorization of 7575 is 1, 3, 5, 5, 101.
- Factorize\( (120) = \) \(1\times 2\times 2\times 2\times 3\times 5\)
- Factorize\( (7575) = \) \(1\times 3\times 5\times 5\times 101\)
Now we need to find any which are common for each number (1, 3, 5) and multiply these numbers together.
\(GCF(120, 7575) = 1\times 3\times 5 = 15\).
Greatest Common Factor of 120 and 7575 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 7575 leaving a remainder zero is 1, 3, 5, 15, 25, 75, 101, 303, 505, 1515, 2525, 7575
As you can see, 15 is the greatest and common number that 120 and 7575 divides into.
So the greatest common factor 120 and 7575 is 15.
\(GCF(120, 7575) = 15\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
