Question 101
To determine the number of positive divisors of a number, it suffices to factor it into powers of distinct primes and multiply the successors of the exponents. For example, $2016=2^{5} \cdot 3^{2} \cdot 5^{1}$ has $(5+1)(2+1)(1+1)=36$ positive divisors. Consider the number $n=2^{7} \cdot 3^{4}$.
a) Determine the number of positive divisors of $n^{2}$.
b) How many divisors of $n^{2}$ are greater than $n$?
c) How many divisors of $n^{2}$ are greater than $n$ and are not multiples of $n$?
a) Determine the number of positive divisors of $n^{2}$.
b) How many divisors of $n^{2}$ are greater than $n$?
c) How many divisors of $n^{2}$ are greater than $n$ and are not multiples of $n$?