Write a program to find the sum of digits of an integer number, input by the user.

Programming Exercises · Q7

Q. Write a program to find the sum of digits of an integer number, input by the user.

Punjab PsebTextbookSubjective· 3mImportance★★★★★est

92% · 36/39 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Concept understanding — Digit Sum Calculation

Digit Sum Calculation

The Intuition

Imagine you have a pile of coins. You want to know roughly how many there are, but you don't care about the exact number — you just want a quick sense of the total. One lazy way: count the coins, but whenever you get to 9, you "wrap around" back to 0 and remember you did that. The number you end up with (0 through 8) is a kind of "remainder" of the total count when divided by 9.

Digit sum works the same way for numbers. Instead of adding the actual value of each digit (like 3 in 300 means three hundred), you just add the digits themselves as if they were single-digit numbers. Then you keep doing that until you get a single digit. That final digit is the digit sum (also called the digital root).

Why does this matter? Because the digit sum of a number is exactly the remainder when you divide that number by 9 — except that if the remainder is 0, the digit sum is 9 (not 0). This is the basis of the ancient technique of "casting out nines," used for centuries to check arithmetic.

The Precise Statement

Definition: The digit sum (or digital root) of a positive integer is the single-digit value obtained by repeatedly summing its digits until only one digit remains.

Example: For 347:

Step 1: $3 + 4 + 7 = 14$
Step 2: $1 + 4 = 5$

So the digit sum of 347 is 5.

Example: For 999:

Step 1: $9 + 9 + 9 = 27$
Step 2: $2 + 7 = 9$

Digit sum is 9.

Example: For 1000:

Step 1: $1 + 0 + 0 + 0 = 1$

Digit sum is 1.

\text{Digit sum}(n) = \begin{cases} 9 & \text{if } n \bmod 9 = 0 \text{ and } n \neq 0 \\ n \bmod 9 & \text{otherwise} \end{cases}

Why It Works

The key insight: any number can be written as a sum of its digits multiplied by powers of 10. For example:

347 = 3 \times 100 + 4 \times 10 + 7 \times 1

Now, $100 = 99 + 1$ , $10 = 9 + 1$ , and $1 = 0 + 1$ . So:

347 = 3 \times (99 + 1) + 4 \times (9 + 1) + 7 \times 1

= (3 \times 99 + 4 \times 9) + (3 + 4 + 7)

The first bracket is clearly divisible by 9. So the remainder when 347 is divided by 9 is exactly the remainder of $(3 + 4 + 7) = 14$ when divided by 9. And $14 \bmod 9 = 5$ , which matches.

Note

This works because $10 \equiv 1 \pmod{9}$ , so every power of 10 is also $\equiv 1 \pmod{9}$ . Therefore, a number and its digit sum are always congruent modulo 9.

Common Mistake …

Start your 14-day free trial to unlock the full solution →

Peel the digits off with % 10 (last digit) and // 10 (remove it), adding each digit to a running sum:

num = int(input("Enter a number: "))
n = abs(num)              # handle a negative input gracefully
digit_sum = 0
while n > 0:
    digit_sum += n % 10
    n = n // 10
print("Sum of digits:", digit_sum)

Enter a number: 6789
Sum of digits: 30
``` …

Start your 14-day free trial to unlock the full solution →

Extract the last digit with n % 10, drop it with n // 10, and accumulate until n becomes 0 — the classic digit-manipulation while loop.

The idea. The modulo and integer-division operators are a natural digit toolkit: n % 10 yields the last digit, and n // 10 gives the number without that digit. Repeating the pair until the number is exhausted visits every digit exactly once — and since we cannot know beforehand how many digits the user's number has, an indefinite while loop (not a counted for) is the right construct.

Algorithm

Input the number; take its absolute value (so a negative input still works).
Set digit_sum = 0.
While n > 0: add n % 10 to digit_sum; set n = n // 10.
Print digit_sum.

Program

num = int(input("Enter a number: "))

n = abs(num)
digit_sum = 0
while n > 0:
    digit_sum += n % 10
    n = n // 10

print("Sum of digits:", digit_sum)

Sample run

Enter a number: 6789
Sum of digits: 30

Trace for 6789

n at start of pass	n % 10	digit_sum	n // 10
6789	9	9	678
678	8	17	67

Start your 14-day free trial to unlock the full solution →

←Previous questionQ6 — Write a program to find the sum of 1+ 1/8 + 1/27......1/n³, where n is…→Next questionQ8 — Write a function that checks whether an input number is a palindrome o…

Q.Write a program to find the sum of digits of an integer number, input by the user.

🎓Unlock everything free for 14 days

Unlock everything free for 14 days