Finding the gcd

Given prime factorizations of positive integers a and b,

$$a \;=\; p_1^{e_1} p_2^{e_2} \cdots p_r^{e_r}, \;\;\;\;\; b \;=\; p_1^{f_1} p_2^{f_2} \cdots p_r^{f_r},$$

where some e_i, f_i may be 0.

Then gcd(a,b) = .

Example: gcd(255, 675) = = 3 * 5 = 15

However, factoring is not a polynomial time algorithm.