This is a problem from TOMATO Objective 94 based on number of divisors. This problem is helpful for ISI Entrance Exam. Try out the problem. (By Akash Singha Roy)
Problem: TOMATO Objective 94
Number of divisors of $ 2700 $
Solution:
$ 2700 = 2^2 \times 3^3\times 5^2 $
Hence, any divisor of $2700 $ must be of the form $2^{a_1} \times 3^{a_2} \times 5^{a_3} $ where $0<=a_1<=2, 0<=a_2<=3, 0<=a_3<=2 $
Therefore, by the Multiplication Principle of Counting, the number of divisors of $ 2700 = (2+1) \times (3+1)\times (2+1) = 36 $
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