Greatest Common Factor of 210 and 315
GCF(210, 315) = 105, Greatest common factor of 210 and 315 is 105. 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 210 and 315. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 210 and 315 by prime factorization method
We will first find the prime factorization of 210 and 315.
Prime Factorization of 210 is 1, 2, 3, 5, 7 and Prime Factorization of 315 is 1, 3, 3, 5, 7.
- Factorize\( (210) = \) \(1\times 2\times 3\times 5\times 7\)
- Factorize\( (315) = \) \(1\times 3\times 3\times 5\times 7\)
Now we need to find any which are common for each number (1, 3, 5, 7) and multiply these numbers together.
\(GCF(210, 315) = 1\times 3\times 5\times 7 = 105\).
Greatest Common Factor of 210 and 315 by matching factors method
List of positive integers factors of 210 leaving a remainder zero is 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
List of positive integers factors of 315 leaving a remainder zero is 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
As you can see, 105 is the greatest and common number that 210 and 315 divides into.
So the greatest common factor 210 and 315 is 105.
\(GCF(210, 315) = 105\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
