How to calculate smallest number with certain number of divisors?

Question

From Project Euler problem 500

The number of divisors of 120 is 16. In fact 120 is the smallest number having 16 divisors.

Find the smalle

Answer 1

Fully functional code.

def find_smallest_number(num):
    number2=0

    if(num%8==0):
        number2=min(2**((num/4)-1)*3**1*5**1 , 2**((num//2)-1)*3**1)
    elif(num%9==0):
        number2=2**((num/9)-1)*3**2*5**2   
    elif(num%2==0 and num%3==0):
        number2=2**((num/6)-1)*3**2*5**1   
    elif((num%4==0)):
        number2=2**((num/4)-1)*3**1*5**1
    elif(num%2==0):
        number2=2**((num/2)-1)*3**1
    else:
        number2=2**(num-1)         

    return number2   


num=32
print("The number of divisors :",num)
result=find_smallest_number(num)
print("The smallest number having",num," divisors:",result)