One way to find the GCF of 144 and 44 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
Here is the prime factorization of 144:
And this is the prime factorization of 44:
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 144 and 44 by multiplying all the matching prime factors to get a GCF of 144 and 44 as 4:
Thus, the GCF of 144 and 44 is: 4