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