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