Calculation of Armstrong Number in Python

Armstrong Numbers in Python is an interesting concept for developers who want to explore number manipulation and mathematical operations. Imagine having the ability to check if a number equals the sum of its digits each raised to the power of the number of digits, demonstrating the use of loops, conditionals, and mathematical expressions effectively. Armstrong Numbers provides a practical way to understand number properties and validate conditions dynamically, enhancing your problem-solving skills.

What is an Armstrong Number?

• An Armstrong Number is a type of number in which the sum of its digits, each raised to the power of the number of digits, equals the number itself.
• It is also known as a Narcissistic number.
• Armstrong Numbers allows you to verify if a number meets this specific criterion, enabling interesting mathematical explorations and coding exercises.
• You can check if a number is an Armstrong Number by summing up its digits raised to the appropriate power and comparing it to the original number.
• For example, 153 is an Armstrong Number because 1³ + 5³ + 3³ = 153.
• Understanding and identifying Armstrong Numbers provides a practical way to work with loops, conditionals, and mathematical operations, making your code more dynamic and enhancing your problem-solving skills.

Mathematical Representation of Armstrong Number

An Armstrong Number of n digits is when the sum of its digits, each raised to the power of the total number of digits, equals the number itself:

abcd… = aⁿ + bⁿ + cⁿ + dⁿ + …

• Here, you take each digit (a, b, c, d, …) of the number and raise it to the power of the total number of digits (n).
• For example, if you have a 3-digit number like 370:

370 = 3³ + 7³ + 0³ = 27 + 343 + 0 = 370

This shows that 370 is an Armstrong Number.

Python Program to check Armstrong Number

def is_armstrong(num):
    num_str = str(num)
    num_digits = len(num_str)
    total = 0

    for digit in num_str:
        total += int(digit) ** num_digits

    return total == num

num1 = 407
if is_armstrong(num1):
    print(num1, "is an Armstrong number.")
else:
    print(num1, "is not an Armstrong number.")

num2 = 372
if is_armstrong(num2):
    print(num2, "is an Armstrong number.")
else:
    print(num2, "is not an Armstrong number.")

Output

407 is an Armstrong number.
372 is not an Armstrong number.

Approaches to Check Armstrong Number in Python

1. Digit by Digit Sum Approach to Check for Armstrong Number

import math

def isArmstrong(num):
	n = num
	numDigits = 0
	sum = 0
	
	# Find number of digits in num
	while n > 0:
		n //= 10
		numDigits += 1
	
	n = num
	
	# Calculate sum of digits raised to the power of numDigits
	while n > 0:
		digit = n % 10
		sum += math.pow(digit, numDigits)
		n //= 10
	
	# Check if num is Armstrong number or not
	if sum == num:
		return True
	return False

num1 = 407
if isArmstrong(num1):
	print(num1, "is an Armstrong number.")
else:
	print(num1, "is not an Armstrong number.")

num2 = 372
if isArmstrong(num2):
	print(num2, "is an Armstrong number.")
else:
	print(num2, "is not an Armstrong number.")

Explanation

• In the above code, first of all, in the isArmstrong() function, we have found the number of digits in the given number and stored it in the numDigits variable.
• Then, we extracted each digit from the given numbers num1 and num2, raised it to the power of the number of digits, and added it to the sum variable.
• If the sum is evaluated to the given number, then it isanArmstrongnumber;otherwise, it is not.

Output

407 is an Armstrong number.
372 is not an Armstrong number.

2. Python program to check if a number is an Armstrong number in return statement

def is_armstrong_number(number):
	return sum(int(digit)**len(str(number)) for digit in str(number)) == number

number = 1634
if is_armstrong_number(number):
	print(f"{number} is an Armstrong number")
else:
	print(f"{number} is not an Armstrong number")

Explanation

• In the above code, the function is_armstrong_number calculates the sum of each digit raised to the power of the number of digits in the number using a generator expression and the sum() function.
• It then compares this sum to the original number to determine if it's an Armstrong number.

Output

1634 is an Armstrong number

3. Check Armstrong number of n digits using a while loop

number = 54748

# Changing num variable to string
order = len(str(number))

sum = 0

temp = number
while temp > 0:
   digit = temp % 10
   sum += digit ** order
   temp //= 10

if number == sum:
   print(number,"is an Armstrong number")
else:
   print(number,"is not an Armstrong number")

Explanation

• The code checks if the number (54748) is an Armstrong Number.
• It calculates the sum of each digit raised to the power of the number of digits (order).
• If this sum matches the original number, it prints that it is an Armstrong Number; otherwise, it indicates that it is not.

Output

54748 is an Armstrong number

4. Check Armstrong number of n digits using functions

# Function to calculate x raised to the power y
def power(a, b):
	
	if b == 0:
		return 1
	if b % 2 == 0:
		return power(a, b // 2) * power(a, b // 2)
		
	return a * power(a, b // 2) * power(a, b // 2)

# Function to calculate the order of the number
def order(a):

	# Variable to store the number
	n = 0
	while (a != 0):
		n = n + 1
		a = a // 10
		
	return n

# Function to check whether the given number is an Armstrong number or not
def isArmstrong(a):
	
	n = order(a)
	temp = a
	sum1 = 0
	
	while (temp != 0):
		r = temp % 10
		sum1 = sum1 + power(r, n)
		temp = temp // 10

	# If condition satisfies
	return (sum1 == a)

# Driver code
a = 370
print(isArmstrong(a))

a = 1253
print(isArmstrong(a))    

Explanation

• In the above code, power(a, b) is a recursive function that calculates the power of a number a raised to the exponent b.
• The order(a) function calculates the order of a number, i.e., the number of digits in it, whereas the Armstrong (a) function checks if the number a is an Armstrong number by summing the powers of its digits and comparing it to the original number.

Output

True
False   

5. Check Armstrong number of n digits using Recursion

def getSum(num):
    if num == 0:
        return num
    else:
        return pow((num % 10), order) + getSum(num // 10)  

num = 371

# Order of the input
order = len(str(num))

# Call the function
sum_val = getSum(num) 

if sum_val == num:
    print('It is an Armstrong number')
else:
    print('It is not an Armstrong number')
 

Explanation

• The code uses a recursive function (getSum) to check if a number is an Armstrong Number.
• It calculates the sum of each digit raised to the power of the total number of digits (order).
• If this sum matches the original number, it prints that it is an Armstrong Number; otherwise, it indicates that it is not.

Output

It is an Armstrong number

6. Check Armstrong Number Using List Comprehension

# Function to check if a number is an Armstrong number using list comprehension
def is_armstrong(num):
    """
    Function to check whether a given number is an Armstrong number.
    :param num: Integer number to check
    :return: True if the number is Armstrong, False otherwise
    """
    power = len(str(num))  # Get the number of digits
    return num == sum(int(digit) ** power for digit in str(num))  # List comprehension

# Driver code
if __name__ == "__main__":
    # Test cases
    numbers = [153, 9474, 370, 1253]

    for num in numbers:
        print(f"{num} is Armstrong: {is_armstrong(num)}") 
    

Explanation

• Function Definition: Compares the original number with the sum of its digits raised to the power of its length.
• List Comprehension: Efficiently computes the required sum in one line.
• Driver Code: Ensures code runs only when executed directly.
• Output Logic: Iterates through the list and prints Armstrong status.

Output

153 is Armstrong: True
9474 is Armstrong: True
370 is Armstrong: True
1253 is Armstrong: False

# Function to check if a number is an Armstrong number using map() and lambda
is_armstrong = lambda num: num == sum(map(lambda x: int(x) ** len(str(num)), str(num)))

# Driver code
if __name__ == "__main__":
    # Test cases
    numbers = [407, 9475]

    for num in numbers:
        print(f"{num} is Armstrong: {is_armstrong(num)}") 
    

407 is Armstrong: True
9475 is Armstrong: False

def isArmstrong(num):
	n = num
	numDigits = 0
	sum = 0
	
	# Find number of digits in num
	while n > 0:
		n //= 10
		numDigits += 1
	
	n = num
	
	# Calculate sum of digits raised to the power of numDigits without using pow()
	while n > 0:
		digit = n % 10
		power = 1
		
		# Compute digit^numDigits manually
		for _ in range(numDigits):
			power *= digit
		
		sum += power
		n //= 10
	
	# Check if num is Armstrong number or not
	if sum == num:
		return True
	return False

num1 = 407
if isArmstrong(num1):
	print(num1, "is an Armstrong number.")
else:
	print(num1, "is not an Armstrong number.")

num2 = 372
if isArmstrong(num2):
	print(num2, "is an Armstrong number.")
else:
	print(num2, "is not an Armstrong number.")

407 is an Armstrong number.
372 is not an Armstrong number.

def isArmstrong(num):
    num_str = str(num)  # Convert number to string
    numDigits = len(num_str)  # Count the number of digits
    
    # Compute sum of digits raised to the power of numDigits
    total = sum(int(digit) ** numDigits for digit in num_str)
    
    # Check if num is an Armstrong number
    return total == num

num1 = 153
if isArmstrong(num1):
    print(num1, "is an Armstrong number.")
else:
    print(num1, "is not an Armstrong number.")

num2 = 123
if isArmstrong(num2):
    print(num2, "is an Armstrong number.")
else:
    print(num2, "is not an Armstrong number.")

153 is an Armstrong number.
123 is not an Armstrong number.