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Find the number of Positive divisors of the number (2010)^2 are ?

Find the number of Positive divisors of the number  (2010)^2 are ?

Grade:12

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
6 years ago
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Samyak Jain
333 Points
5 years ago
First of all factorise 2010 in prime numbers.
So 2010 = 21 * 51 * 31 * 671  
There is one 2 in the prime factorisation of 2010. So we have two choices of selecting 2.
First, to take it and second not to take it.
Similarly we have two choices each of selecting of 5, 3, 67;
either to take the number or to skip it.
\therefore No. of divisors = 2 * 2 * 2 * 2 = 16
The anwer contains different combination of numbers. 
One selection is not to take any of the mentioned prime numbers.
In this case, we indirectly took 1 as a divisor of 2010.

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