Python: Efficiently Obtain All Divisors of a Number - Best Method

When it comes to obtaining all divisors of a number efficiently in Python, there are a few different approaches you can take. However, one of the most efficient methods is to use a simple loop that iterates through all numbers from 1 to the square root of the given number.


import math

def get_divisors(n):
    divisors = []
    for i in range(1, int(math.sqrt(n))+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n // i)
    return divisors

Let's break down how this code works. First, we import the math module so that we can use the sqrt function to obtain the square root of the given number. Next, we define a function called get_divisors that takes in a number n.

Inside the function, we initialize an empty list called divisors to hold all of the divisors we find. We then iterate through all numbers from 1 to the square root of n, checking if each number is a divisor of n using the modulo operator (%).

If a number is a divisor, we add it to our list of divisors. We also check if the divisor is not equal to the square root of n, in which case we add the corresponding factor to our list as well. This ensures that we capture all divisors of n, not just the ones less than the square root.

The use of the sqrt function and the conditional check for the corresponding factor allows us to avoid iterating through all numbers up to n, making this method much more efficient for large numbers.

Overall, if you're looking for a fast and efficient way to obtain all divisors of a number in Python, this method using a simple loop and the sqrt function is definitely one of the best options available.

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