Find the largest divisor of 6006006006 that does not exceed 60,000

Question

factoring it, we have

$6 * 1001*1000001 = 2*3*7*11*13* (100^3+1) = 2*3*7*11*13*101*9901$

with this prime factorization, how do you check the largest divisor without too much guessing and checking?

Answer 1

One way is to look for targets to get close to and just use your own numerical nous. Here, the obvious targets are the given $60000$, and $6006006006/60000 \approx 100100$.

$2\cdot3\cdot9901=59406$.

For this instance, start with $60000=10000\cdot6$ and notice that $9901$ is a little less than $10000$, then look for $6$.

With a more complicated factorization it's worth checking quite a few options.