Greatest Common Factor of 208 and 702
GCF(208, 702) = 26, Greatest common factor of 208 and 702 is 26. 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 208 and 702. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 208 and 702 by prime factorization method
We will first find the prime factorization of 208 and 702.
Prime Factorization of 208 is 1, 2, 2, 2, 2, 13 and Prime Factorization of 702 is 1, 2, 3, 3, 3, 13.
- Factorize\( (208) = \) \(1\times 2\times 2\times 2\times 2\times 13\)
- Factorize\( (702) = \) \(1\times 2\times 3\times 3\times 3\times 13\)
Now we need to find any which are common for each number (1, 2, 13) and multiply these numbers together.
\(GCF(208, 702) = 1\times 2\times 13 = 26\).
Greatest Common Factor of 208 and 702 by matching factors method
List of positive integers factors of 208 leaving a remainder zero is 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
List of positive integers factors of 702 leaving a remainder zero is 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702
As you can see, 26 is the greatest and common number that 208 and 702 divides into.
So the greatest common factor 208 and 702 is 26.
\(GCF(208, 702) = 26\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
