Greatest Common Factor of 100 and 171
GCF(100, 171) = 1, Greatest common factor of 100 and 171 is 1. 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 171. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 100 and 171 by prime factorization method
We will first find the prime factorization of 100 and 171.
Prime Factorization of 100 is 1, 2, 2, 5, 5 and Prime Factorization of 171 is 1, 3, 3, 19.
- Factorize\( (100) = \) \(1\times 2\times 2\times 5\times 5\)
- Factorize\( (171) = \) \(1\times 3\times 3\times 19\)
Now we need to find any which are common for each number (1, 1) and multiply these numbers together.
\(GCF(100, 171) = 1\times 1 = 1\).
Greatest Common Factor of 100 and 171 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 171 leaving a remainder zero is 1, 3, 9, 19, 57, 171
As you can see, 1 is the greatest and common number that 100 and 171 divides into.
So the greatest common factor 100 and 171 is 1.
\(GCF(100, 171) = 1\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
