Finding Factors of a Number Efficiently in Python

Determining the factors of a number is a common task in various domains, and Python offers multiple efficient ways to accomplish it.

One optimized approach involves utilizing Python's reduce function along with list comprehension. This concise solution effectively finds all the factors of a given number.

from functools import reduce

def factors(n):
    return set(reduce(
        list.__add__,
        ([i, n//i] for i in range(1, int(n**0.5)   1) if n % i == 0)))

Rationale:

• The generator expression ([i, n//i] for i in range(1, int(n**0.5) 1) if n % i == 0)) produces pairs of factors [factor1, factor2] where factor1 is less than or equal to the square root of the number n. This optimization reduces the computation time.
• The reduce function concatenates the lists of pairs into a single list, while the set data structure removes any duplicates that may occur in the case of perfect squares.
• For a number n, the list comprehension only needs to loop up to the square root of n because the number itself can always be paired with 1 as a factor.