Greatest Common Factor of 100 and 354
GCF(100, 354) = 2, Greatest common factor of 100 and 354 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 100 and 354. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 100 and 354 by prime factorization method
We will first find the prime factorization of 100 and 354.
Prime Factorization of 100 is 1, 2, 2, 5, 5 and Prime Factorization of 354 is 1, 2, 3, 59.
- Factorize\( (100) = \) \(1\times 2\times 2\times 5\times 5\)
- Factorize\( (354) = \) \(1\times 2\times 3\times 59\)
Now we need to find any which are common for each number (1, 2) and multiply these numbers together.
\(GCF(100, 354) = 1\times 2 = 2\).
Greatest Common Factor of 100 and 354 by matching factors method
List of positive integers factors of 100 leaving a remainder zero is 1, 2, 4, 5, 10, 20, 25, 50, 100
List of positive integers factors of 354 leaving a remainder zero is 1, 2, 3, 6, 59, 118, 177, 354
As you can see, 2 is the greatest and common number that 100 and 354 divides into.
So the greatest common factor 100 and 354 is 2.
\(GCF(100, 354) = 2\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
