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What are the total number of proper divisors for 900?
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM

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 | 04 Jun, 2014, 03:23: PM

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