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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?

 Jan 11, 2022
 #1
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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

 Jan 11, 2022
 #2
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Any of the 6 values of n will give you:

 

81*n ==40 divisors.

Guest Jan 11, 2022

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