Greatest Common Factor of 144 and 10032
GCF(144, 10032) = 48, Greatest common factor of 144 and 10032 is 48. 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 144 and 10032. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 144 and 10032 by prime factorization method
We will first find the prime factorization of 144 and 10032.
Prime Factorization of 144 is 1, 2, 2, 2, 2, 3, 3 and Prime Factorization of 10032 is 1, 2, 2, 2, 2, 3, 11, 19.
- Factorize\( (144) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 3\)
- Factorize\( (10032) = \) \(1\times 2\times 2\times 2\times 2\times 3\times 11\times 19\)
Now we need to find any which are common for each number (1, 2, 2, 2, 2, 3) and multiply these numbers together.
\(GCF(144, 10032) = 1\times 2\times 2\times 2\times 2\times 3 = 48\).
Greatest Common Factor of 144 and 10032 by matching factors method
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
List of positive integers factors of 10032 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 11, 12, 16, 19, 22, 24, 33, 38, 44, 48, 57, 66, 76, 88, 114, 132, 152, 176, 209, 228, 264, 304, 418, 456, 528, 627, 836, 912, 1254, 1672, 2508, 3344, 5016, 10032
As you can see, 48 is the greatest and common number that 144 and 10032 divides into.
So the greatest common factor 144 and 10032 is 48.
\(GCF(144, 10032) = 48\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
