To compute the GCF of two number, you need their prime factorization.
Then, you "build" the GCF by only considering the primes appearing in both factorization, with the smaller exponent possible.
So, to compute the GCF between 6 and 9, you first consider their factorization:
[tex] 6 = 2 \times 3 [/tex]
[tex] 9 = 3^2 = 3 \times 3 [/tex]
So, the only prime appearing in both factorization is 3.
It appears with exponent 1 in the factorization of 6, and with exponent 2 in the factorization of 9. We must choose the smallest, so we choose 1.
So, 3 with exponent 1 is simply 3, and here's your GCF
