What are the total number of proper divisors for 900?

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

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.

Answered by  | 4th Jun, 2014, 03:23: PM