Learn an exciting method

Radhika divides 20 by every number from 1 to 20 for counting the number of total divisors of 20. But she found this method quite boring and tedious. So, she learnt an exciting method to count the number of divisors. Given that she answered correctly to the following questions, what is the answer she submitted?

How many positive divisors does the integer 75 have?


The answer is 6.

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1 solution

It's easy

20 = 2 2 × 5 20={ 2 }^{ 2 }\times 5

then just ( 2 + 1 ) ( 1 + 1 ) = ( 3 ) ( 2 ) = 6 (2+1)(1+1)\\ =(3)(2)\\ =6

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