Greatest common factor of 48 and 72

The GCF of 48 and 72 is 24.
Here is how to find it.
First do the prime factorization of each number:
48 = 6 x 8 = 2 x 3 x 2 x 4 = 2 x 3 x 2 x 2 x 2  or 2⁴ x 3
72 = 8 x 9 = 2 x 2 x 2 x 3 x 3 or 2³ x 3²
When we find the Greatest Common Factor we only use what they have in common and to the least power  (isn't that interesting)
So  we have 2³ and 2⁴  but we have to use the least power which is 2³
We have 3 (in 48) and 3² (in 72) but we can only use 3 (the least power  3=3¹) 
Multiply those two numbers  2³ x 3 and you get 8 x 3 which is 24 and is the GCF.