Greatest Common Factor of 68 and 34
GCF(68, 34) = 34, Greatest common factor of 68 and 34 is 34. 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 68 and 34. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 68 and 34 by prime factorization method
We will first find the prime factorization of 68 and 34.
Prime Factorization of 68 is 1, 2, 2, 17 and Prime Factorization of 34 is 1, 2, 17.
- Factorize\( (68) = \) \(1\times 2\times 2\times 17\)
- Factorize\( (34) = \) \(1\times 2\times 17\)
Now we need to find any which are common for each number (1, 2, 17) and multiply these numbers together.
\(GCF(68, 34) = 1\times 2\times 17 = 34\).
Greatest Common Factor of 68 and 34 by matching factors method
List of positive integers factors of 68 leaving a remainder zero is 1, 2, 4, 17, 34, 68
List of positive integers factors of 34 leaving a remainder zero is 1, 2, 17, 34
As you can see, 34 is the greatest and common number that 68 and 34 divides into.
So the greatest common factor 68 and 34 is 34.
\(GCF(68, 34) = 34\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
