Check whether product of \'n\' numbers is even or odd in Python

In this article, we explore different methods to check whether the product of n numbers is even or odd. A number that is divisible by 2 is known as an even number, otherwise it is an odd number.

For example, 14 and 12 are two even numbers, their product 168 is even. Numbers 9 and 5 are odd, their product 45 is odd. Consider one even number 2 and one odd number 3 − their product 6 is even.

Mathematical Facts

Understanding these mathematical rules helps us determine if a product is even or odd −

• The product of two even numbers is always even
• The product of two odd numbers is always odd
• The product of one even and one odd number is always even

Key insight: If any number in the set is even, the entire product will be even.

Method 1: Using Bitwise AND Operator

The bitwise & operation checks the least significant bit (LSB). For any number, num & 1 returns 0 if even, 1 if odd −

def check_product_bitwise(numbers):
    for num in numbers:
        if not num & 1:  # If LSB is 0, number is even
            return "Even"
    return "Odd"
   
numbers = [5, 7, 4, 2, 6]
result = check_product_bitwise(numbers)
print("Product of the numbers:", result)

Product of the numbers: Even

Method 2: Calculate Actual Product

This approach computes the actual product and checks if it's divisible by 2 −

numbers = [2, 5, 9, 7, 2]
product = 1

for num in numbers:
    product = product * num
   
if product % 2 == 0:
    print("Product of numbers is Even")
else:
    print("Product of numbers is Odd")

Product of numbers is Even

Method 3: Check for Even Number Presence

Based on mathematical facts, we only need to check if any even number exists −

def check_product_presence(numbers):
    for num in numbers:
        if num % 2 == 0:
            return "Even"
    return "Odd"
   
numbers = [21, 5, 9, 7, 27]
result = check_product_presence(numbers)
print("Product of numbers:", result)

Product of numbers: Odd

Method 4: Count Even Numbers

If one or more even numbers exist, the product is guaranteed to be even −

def check_product_count(numbers):
    even_count = 0
    for num in numbers:
        if num % 2 == 0:
            even_count += 1
    
    if even_count >= 1:
        return "Even"
    return "Odd"
  
numbers = [75, 97, 49, 61, 28]
result = check_product_count(numbers)
print("Product of numbers:", result)

Product of numbers: Even

Performance Comparison

Conclusion

The most efficient approach is checking for even number presence, as it stops immediately when an even number is found. Use bitwise operations for performance-critical applications, or the modulo approach for better readability.