TOMATO Objective 94

Akash Singha Roy

Problem:

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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