For odd values of M the divisors can be grouped in couples such that

sum of logs in each couple will be M:

1,10^M; 2, 10^M/2;....d, 10^M/d.

Clearly there are .5*(M+1)^2 couples, so

.**5*(M+1)^2*M=792**

**and M=11**

For even values of M the formula is slightly different, but it is immaterial now.

*Edited on ***August 1, 2014, 3:09 pm**