How to quickly find out how many divisors a number has?

First of all, use the product of prime numbers such as 2, 3, 5, 7, 11, 13, etc. to express this number.

For example, 24 = 2*2*2*3 = 2³ * 3, then add one to the exponent of each prime number and then multiply it to get the divisor of this number, such as (3+1)*(1+1)=4 *2=8, which means that 24 has 8 divisors.

E.g: 

1200000 = 2^7 * 3 * 5^5;

So the approximate number is (7+1) * (1+1) * (5+1) = 8 * 2 * 6 = 96;