Instead of finding the GCF, you can simplify with mental math.
If you notice they are both divisible by any number, divide them both by this number to simplify until they share no common factors.
252 and 288 are both divisible by 2.
252/288 = 126/144
126 and 144 are both divisible by 2.
126/144 = 63/72
63 and 72 are both divisible by 3.
63/72 = 21/24
21 and 24 are both divisible by 3.
21/24 = 7/8
