If we have the product of 3 primes, two of them large and one small, can we find the small one through factorization?

Question

If we have the product of 3 primes, ABs two of them large: A, B and one small: s We don t know the product of AB, (Given that if we knew AB we couldn t factorize it, because of the size and the computational complexity of the problem.) can we find the small number s through factorization? Is there an algorithm with less computational complexity than factoization of AB, to find s in ABs, when we don t know AB?

Answer 1

You could use elliptic curve factorization, although it is better when the number also has many factors:

https://en.wikipedia.org/wiki/Lenstra_elliptic_curve_factorization

Answer 2

If $s$ is known to be $\le N$, where $N$ is not too big, you can take the gcd of $ABs$ and the product of all primes $\le N$.