Greatest Common Factor of 28 and 408
GCF(28, 408) = 4, Greatest common factor of 28 and 408 is 4. 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 28 and 408. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 28 and 408 by prime factorization method
We will first find the prime factorization of 28 and 408.
Prime Factorization of 28 is 1, 2, 2, 7 and Prime Factorization of 408 is 1, 2, 2, 2, 3, 17.
- Factorize\( (28) = \) \(1\times 2\times 2\times 7\)
- Factorize\( (408) = \) \(1\times 2\times 2\times 2\times 3\times 17\)
Now we need to find any which are common for each number (1, 2, 2) and multiply these numbers together.
\(GCF(28, 408) = 1\times 2\times 2 = 4\).
Greatest Common Factor of 28 and 408 by matching factors method
List of positive integers factors of 28 leaving a remainder zero is 1, 2, 4, 7, 14, 28
List of positive integers factors of 408 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
As you can see, 4 is the greatest and common number that 28 and 408 divides into.
So the greatest common factor 28 and 408 is 4.
\(GCF(28, 408) = 4\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
