What are the total number of proper divisors for 900?

900 can be written as 2²x3²x5²=900

 

Now the way to select a proper divisor would mean that we have to include all the powers for each factor including zero.
Hence, for 2 we can have 2⁰ , 2¹ , 2²

 

which gives us 3 options.

Similarly for 3, we can have options from 3⁰ , 3¹ , 3²

And also for 5, we will also have 3 options.

 

Hence, the total number of divisors=3x3x3=27

 

This would however include the case of the number itself and 1.
 Hence, we must subtract 2 divisors from this to get 27-2=25.