For some positive integer n, the number 110n^3 has 110 positive integer divisors, including 1 and the number 110n^3. How many positive integer divisors does the number \(81n\) have?
110 = 2 * 5 * 11
So n can have six possible values:
2 * 5^3 = 250
2 * 11^3 = 2662
5 * 2^3 = 40
5 * 11^3 = 6655
11 * 2^3 = 88
11 * 5^3 = 1375
For any of these n, 110*n^3 will have 110 divisors
Any of the 6 values of n will give you:
81*n ==40 divisors.
