Greatest Common Factor of 68 and 2754
GCF(68, 2754) = 34, Greatest common factor of 68 and 2754 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 2754. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 68 and 2754 by prime factorization method
We will first find the prime factorization of 68 and 2754.
Prime Factorization of 68 is 1, 2, 2, 17 and Prime Factorization of 2754 is 1, 2, 3, 3, 3, 3, 17.
- Factorize\( (68) = \) \(1\times 2\times 2\times 17\)
- Factorize\( (2754) = \) \(1\times 2\times 3\times 3\times 3\times 3\times 17\)
Now we need to find any which are common for each number (1, 2, 17) and multiply these numbers together.
\(GCF(68, 2754) = 1\times 2\times 17 = 34\).
Greatest Common Factor of 68 and 2754 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 2754 leaving a remainder zero is 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 81, 102, 153, 162, 306, 459, 918, 1377, 2754
As you can see, 34 is the greatest and common number that 68 and 2754 divides into.
So the greatest common factor 68 and 2754 is 34.
\(GCF(68, 2754) = 34\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
