Here’s a cool trick to find the number of divisors of any number easily. First of all find the prime factors of that number. Say we want to do it for 1000.

1000 = 2³ * 5³

Now we can say that all proper divisors of 1000 will be in the form of 2^a * 5^b, where a can be 0, 1, 2 or 3 and b can be 0, 1, 2 or 3.

So you basically can choose from 4 possible options for the first power and 4 for the second power as well, so in total there are 4*4 = 16 divisors of 1000 (that’s including 1 and itself).

Rohit Kumar UmraoHi Daniel ,

I thinks this is the upper bound of the number of divisors . the result is always less than the solution given by you.

Thanks

Rohit