Greatest Common Factor of 172 and 10414
GCF(172, 10414) = 2, Greatest common factor of 172 and 10414 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 172 and 10414. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 172 and 10414 by prime factorization method
We will first find the prime factorization of 172 and 10414.
Prime Factorization of 172 is 1, 2, 2, 43 and Prime Factorization of 10414 is 1, 2, 41, 127.
- Factorize\( (172) = \) \(1\times 2\times 2\times 43\)
- Factorize\( (10414) = \) \(1\times 2\times 41\times 127\)
Now we need to find any which are common for each number (1, 2) and multiply these numbers together.
\(GCF(172, 10414) = 1\times 2 = 2\).
Greatest Common Factor of 172 and 10414 by matching factors method
List of positive integers factors of 172 leaving a remainder zero is 1, 2, 4, 43, 86, 172
List of positive integers factors of 10414 leaving a remainder zero is 1, 2, 41, 82, 127, 254, 5207, 10414
As you can see, 2 is the greatest and common number that 172 and 10414 divides into.
So the greatest common factor 172 and 10414 is 2.
\(GCF(172, 10414) = 2\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
