Originally Posted by

**BobP** If you were to use the suggested $\displaystyle 2^{x}.3^{y}.5^{z},$ a divisor would be the product of 0,1,2,... or x 2's, 0,1,2,... or y 3's and 0,1,2,... or z 5's. That would give you a possible (x+1)(y+1)(z+1) divisors. You would need that to equal 768.

I think though it's necessary to include higher primes.

If we assume that the divisors are of the form $\displaystyle 2^{a}.3^{b}.5^{c}.7^{d}.\dots$ then we would need

$\displaystyle (a+1)(b+1)(c+1)(d+1) \dots = 768.$ WHY?

Since $\displaystyle 768=2^{8}.3,$ the best that I can come up with for the moment, subject to further investigation, is,

$\displaystyle a=2, b=c=d=e=f=g=h=I=1$ which produces the number $\displaystyle 2^{2}.3.5.7.11.13.17.19.23=446185740.$