How do you calculate if a number is a palindrome?

You calculate if a number is a palindrome by comparing the original number to its reversed version. If they are the same, the number is a palindrome.

Here's a breakdown of the process:

1. Reverse the Number: The core of the calculation involves reversing the order of the digits in the number.
2. Compare to Original: After reversing, you compare the reversed number to the original number.

Here's a more detailed look with examples:

Methods to Determine Palindrome:

• String Conversion Method:

  1. Convert the number to a string.
  2. Reverse the string.
  3. Compare the reversed string with the original string.

  def is_palindrome_string(number):
    """Checks if a number is a palindrome using string conversion."""
    num_str = str(number)
    reversed_str = num_str[::-1]  # Reverses the string
    return num_str == reversed_str
  
  # Example usage:
  print(is_palindrome_string(121))   # Output: True
  print(is_palindrome_string(123))   # Output: False

• Mathematical Method (Without String Conversion):

  1. Store the original number.
  2. Reverse the number mathematically. This involves extracting the last digit, adding it to a reversed number (multiplied by 10 to shift digits), and then removing the last digit from the original number.
  3. Compare the reversed number with the original number stored in step 1.

  def is_palindrome_math(number):
    """Checks if a number is a palindrome using mathematical operations."""
    original_number = number
    reversed_number = 0
  
    while number > 0:
      last_digit = number % 10
      reversed_number = (reversed_number * 10) + last_digit
      number = number // 10  # Integer division to remove the last digit
  
    return original_number == reversed_number
  
  # Example usage:
  print(is_palindrome_math(121))   # Output: True
  print(is_palindrome_math(123))   # Output: False

Example:

Let's consider the number 121:

• String Method:

  • String Conversion: 121
  • Reversed String: 121
  • Comparison: 121 == 121 (True - Palindrome)

• Mathematical Method:

  • Original number: 121
  • Iteration 1: last_digit = 1, reversed_number = (0 * 10) + 1 = 1, number = 12
  • Iteration 2: last_digit = 2, reversed_number = (1 * 10) + 2 = 12, number = 1
  • Iteration 3: last_digit = 1, reversed_number = (12 * 10) + 1 = 121, number = 0
  • Comparison: 121 == 121 (True - Palindrome)