Armstrong Number in Python

The question

Read a positive integer and print whether it is an Armstrong number: the sum of each digit raised to the power of the number of digits equals the number itself (153 = 1³ + 5³ + 3³).

The code

n = int(input())
k = len(str(n))
total = 0
temp = n
while temp > 0:
    total += (temp % 10) ** k
    temp //= 10
if total == n:
    print(n, "is an Armstrong number")
else:
    print(n, "is not an Armstrong number")

How it works

1. 1k = len(str(n)) counts the digits — 3 for 153, 4 for 1634.
2. 2Work on a copy (temp) so n is still available for the final comparison.
3. 3Add (temp % 10) ** k for every digit, removing digits with temp //= 10.
4. 4Compare the total with n.

Dry run: is 153 an Armstrong number?

153 has 3 digits, so k = 3. Each pass of the while loop takes the last digit, raises it to the power 3 and adds it to total.

temp is now 0, so the loop stops. total = 153 = n, so 153 is an Armstrong number.

Armstrong number in Python using a for loop

Turn the number into a string and the for loop hands you one digit at a time — no % or // needed. int(d) changes each character back into a number.

n = int(input())
digits = str(n)
k = len(digits)
total = 0
for d in digits:
    total += int(d) ** k
if total == n:
    print(n, "is an Armstrong number")
else:
    print(n, "is not an Armstrong number")

153

153 is an Armstrong number

Print all Armstrong numbers between 100 and 999

The same digit loop, placed inside a for loop that tries every 3-digit number. Every number here has three digits, so the power is fixed at 3.

for n in range(100, 1000):
    total = 0
    temp = n
    while temp > 0:
        total += (temp % 10) ** 3
        temp //= 10
    if total == n:
        print(n)

(no input)

153
370
371
407

Armstrong number in Python using a function

sum() with a generator does the whole digit loop in one line. The function returns True or False, so it can be reused — for example to test every number in a range.

def is_armstrong(n):
    s = str(n)
    return n == sum(int(d) ** len(s) for d in s)

n = int(input())
if is_armstrong(n):
    print(n, "is an Armstrong number")
else:
    print(n, "is not an Armstrong number")

9474

9474 is an Armstrong number

Questions students ask

What is an Armstrong number in Python?

It is a number that equals the sum of its own digits, each raised to the power of the number of digits. 153 has three digits and 1³ + 5³ + 3³ = 1 + 125 + 27 = 153, so 153 is an Armstrong number. In Python you check it by taking the digits out one by one with % 10 and // 10.

Which numbers are Armstrong numbers?

The 3-digit Armstrong numbers are 153, 370, 371 and 407. The 4-digit ones are 1634, 8208 and 9474. Every single-digit number is also an Armstrong number, because a digit raised to the power 1 is itself.

What do 153 % 10 and 153 // 10 give in Python?

153 % 10 gives 3, the last digit. 153 // 10 gives 15, the number with its last digit removed. Repeating the two operations walks through every digit: 3, then 5, then 1.

Is 1634 an Armstrong number?

Yes. It has four digits, so each digit is raised to the power 4: 1 + 1296 + 81 + 256 = 1634. A program that always cubes the digits gets this one wrong.

Is an Armstrong number the same as a narcissistic number?

Yes. Narcissistic number and pluperfect digital invariant are other names for the same idea: a number equal to the sum of its own digits, each raised to the power of the number of digits.

More in while loop

• Python Program to Find the Sum of Digits of a Number
• Python Program to Reverse a Number
• Python Program to Convert Decimal to Binary