Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Number of divisors and Integers.
The number of different factors of 6000, where 1 and 6000 are also considered as divisors of 6000, is
Integers
Number of divisors
Exponents
Answer: 40
B.Stat Objective Problem 97
Challenges and Thrills of Pre-College Mathematics by University Press
Here 6000=(2)(2)(2)(2)(3)(5)(5)(5)
number of divisors of 6000 =(4+1)(1+1)(3+1) where number of divisors=(a+1)(b+1)(c+1) for n=\(p_1^{a}p_2^{b}p_3^{c}\) as \(p_1,p_2,p_3\) are primes
=(5)(2)(4)=40.
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