When working with factor pairs in Python, it is important to consider all possible combinations, including negative factors. In this article, we will explore three different approaches to solve this problem.

Approach 1: Using a Nested Loop

def factor_pairs(n):
    pairs = []
    for i in range(1, abs(n) + 1):
        if n % i == 0:
            pairs.append((i, n // i))
            pairs.append((-i, -n // i))
    return pairs

number = int(input("Enter a number: "))
pairs = factor_pairs(number)
print("Factor pairs:", pairs)

In this approach, we use a nested loop to iterate through all possible factors of the given number. We start from 1 and go up to the absolute value of the number. For each factor, we check if it divides the number evenly using the modulo operator (%). If it does, we add both the positive and negative factor pairs to a list. Finally, we return the list of factor pairs.

Approach 2: Using List Comprehension

def factor_pairs(n):
    return [(i, n // i) for i in range(1, abs(n) + 1) if n % i == 0] + [(-i, -n // i) for i in range(1, abs(n) + 1) if n % i == 0]

number = int(input("Enter a number: "))
pairs = factor_pairs(number)
print("Factor pairs:", pairs)

In this approach, we use list comprehension to generate the factor pairs directly. We iterate through the range of factors and use a conditional statement to filter out the factors that do not divide the number evenly. We then add both the positive and negative factor pairs to the resulting list.

Approach 3: Using a Generator Function

def factor_pairs(n):
    for i in range(1, abs(n) + 1):
        if n % i == 0:
            yield (i, n // i)
            yield (-i, -n // i)

number = int(input("Enter a number: "))
pairs = list(factor_pairs(number))
print("Factor pairs:", pairs)

In this approach, we use a generator function to generate the factor pairs on-the-fly. We iterate through the range of factors and use a conditional statement to yield the factor pairs that divide the number evenly. We then convert the generator object to a list to display the factor pairs.

After analyzing these three approaches, it is evident that the second approach using list comprehension is the most concise and efficient solution. It achieves the same result as the other approaches but with less code and better performance. Therefore, the second approach is the recommended solution for finding all possible factor pairs, including negatives, in Python.