Greatest Common Factor of 120 and 1050
GCF(120, 1050) = 30, Greatest common factor of 120 and 1050 is 30. 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 1050. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 120 and 1050 by prime factorization method
We will first find the prime factorization of 120 and 1050.
Prime Factorization of 120 is 1, 2, 2, 2, 3, 5 and Prime Factorization of 1050 is 1, 2, 3, 5, 5, 7.
- Factorize\( (120) = \) \(1\times 2\times 2\times 2\times 3\times 5\)
- Factorize\( (1050) = \) \(1\times 2\times 3\times 5\times 5\times 7\)
Now we need to find any which are common for each number (1, 2, 3, 5) and multiply these numbers together.
\(GCF(120, 1050) = 1\times 2\times 3\times 5 = 30\).
Greatest Common Factor of 120 and 1050 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 1050 leaving a remainder zero is 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050
As you can see, 30 is the greatest and common number that 120 and 1050 divides into.
So the greatest common factor 120 and 1050 is 30.
\(GCF(120, 1050) = 30\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
