Greatest Common Factor of 172 and 144
GCF(172, 144) = 4, Greatest common factor of 172 and 144 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 172 and 144. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 172 and 144 by prime factorization method
We will first find the prime factorization of 172 and 144.
Prime Factorization of 172 is 1, 2, 2, 43 and Prime Factorization of 144 is 1, 2, 2, 2, 2, 3, 3.
- Factorize\( (172) = \) \(1\times 2\times 2\times 43\)
- Factorize\( (144) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 3\)
Now we need to find any which are common for each number (1, 2, 2) and multiply these numbers together.
\(GCF(172, 144) = 1\times 2\times 2 = 4\).
Greatest Common Factor of 172 and 144 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 144 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
As you can see, 4 is the greatest and common number that 172 and 144 divides into.
So the greatest common factor 172 and 144 is 4.
\(GCF(172, 144) = 4\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
