Mathematics - Permutation & Combination Question with Solution | TestHub

$(2008{)}^8=2^{24}\times 251^8$ has $25\times 9=225$ positive divisors, including $(2008{)}^4=\sqrt{(2008{)}^8}$. There is a one-to-one correspondence between the positive divisors less than $(2008{)}^4$ and those larger than $(2008{)}^4$. It follows that there are $\frac{1}{2}(225-1)=112$ positive divisors less than $(2008{)}^4$.