# Finding sum of digits of a number until sum becomes single digit

• Difficulty Level : Medium
• Last Updated : 13 Jun, 2022

Given a number n, we need to find the sum of its digits such that:

```If n < 10
digSum(n) = n
Else
digSum(n) = Sum(digSum(n))```

Examples :

```Input : 1234
Output : 1
Explanation : The sum of 1+2+3+4 = 10,
digSum(x) == 10
Hence ans will be 1+0 = 1

Input : 5674
Output : 4 ```
Recommended Practice

A brute force approach is to sum all the digits until the sum < 10.
Flowchart: Below is the brute force program to find the sum.

## C++

 `// C++ program to find sum of` `// digits of a number until` `// sum becomes single digit.` `#include` ` `  `using` `namespace` `std;`   `int` `digSum(``int` `n)` `{` `    ``int` `sum = 0;` `   `  `    ``// Loop to do sum while` `    ``// sum is not less than` `    ``// or equal to 9` `    ``while``(n > 0 || sum > 9)` `    ``{` `        ``if``(n == 0)` `        ``{` `            ``n = sum;` `            ``sum = 0;` `        ``}` `        ``sum += n % 10;` `        ``n /= 10;` `    ``}` `    ``return` `sum;` `}`   `// Driver program to test the above function` `int` `main()` `{` `    ``int` `n = 1234;` `    ``cout << digSum(n);` `    ``return` `0;` `}`

## Java

 `// Java program to find sum of` `// digits of a number until` `// sum becomes single digit.` `import` `java.util.*;`   `public` `class` `GfG {` `    `  `    ``static` `int` `digSum(``int` `n)` `    ``{` `        ``int` `sum = ``0``;`   `        ``// Loop to do sum while` `        ``// sum is not less than` `        ``// or equal to 9` `        ``while` `(n > ``0` `|| sum > ``9``) ` `        ``{` `            ``if` `(n == ``0``) {` `                ``n = sum;` `                ``sum = ``0``;` `            ``}` `            ``sum += n % ``10``;` `            ``n /= ``10``;` `        ``}` `        ``return` `sum;` `    ``}` `    `  `    ``// Driver code` `    ``public` `static` `void` `main(String argc[])` `    ``{` `        ``int` `n = ``1234``;` `        ``System.out.println(digSum(n));` `    ``}` `}`   `// This code is contributed by Gitanjali.`

## Python

 `# Python program to find sum of` `# digits of a number until` `# sum becomes single digit.` `import` `math `   `# method to find sum of digits ` `# of a number until sum becomes ` `# single digit` `def` `digSum( n):` `    ``sum` `=` `0` `    `  `    ``while``(n > ``0` `or` `sum` `> ``9``):` `    `  `        ``if``(n ``=``=` `0``):` `            ``n ``=` `sum` `            ``sum` `=` `0` `        `  `        ``sum` `+``=` `n ``%` `10` `        ``n ``/``=` `10` `    `  `    ``return` `sum`   `# Driver method` `n ``=` `1234` `print` `(digSum(n))`   `# This code is contributed by Gitanjali.`

## C#

 `// C# program to find sum of` `// digits of a number until` `// sum becomes single digit.` `using` `System;`   `class` `GFG {` `    `  `    ``static` `int` `digSum(``int` `n)` `    ``{` `        ``int` `sum = 0;`   `        ``// Loop to do sum while` `        ``// sum is not less than` `        ``// or equal to 9` `        ``while` `(n > 0 || sum > 9) ` `        ``{` `            ``if` `(n == 0)` `            ``{` `                ``n = sum;` `                ``sum = 0;` `            ``}` `            ``sum += n % 10;` `            ``n /= 10;` `        ``}` `        ``return` `sum;` `    ``}` `    `  `    ``// Driver code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `n = 1234;` `        ``Console.Write(digSum(n));` `    ``}` `}`   `// This code is contributed by nitin mittal`

## PHP

 ` 0 || ``\$sum` `> 9)` `    ``{` `        ``if``(``\$n` `== 0)` `        ``{` `            ``\$n` `= ``\$sum``;` `            ``\$sum` `= 0;` `        ``}` `        ``\$sum` `+= ``\$n` `% 10;` `        ``\$n` `= (int)``\$n` `/ 10;` `    ``}` `    ``return` `\$sum``;` `}`   `// Driver Code` `\$n` `= 1234;` `echo` `digSum(``\$n``);`   `// This code is contributed` `// by aj_36` `?>`

## Javascript

 ``

## C

 `// C program to find sum of` `// digits of a number until` `// sum becomes single digit.` `#include`   `int` `digSum(``int` `n)` `{` `    ``int` `sum = 0;` `   `  `    ``// Loop to do sum while` `    ``// sum is not less than` `    ``// or equal to 9` `    ``while``(n > 0 || sum > 9)` `    ``{` `        ``if``(n == 0)` `        ``{` `            ``n = sum;` `            ``sum = 0;` `        ``}` `        ``sum += n % 10;` `        ``n /= 10;` `    ``}` `    ``return` `sum;` `}`   `// Driver program to test the above function` `int` `main()` `{` `    ``int` `n = 1234;` `    ``printf``(``"%d"``,digSum(n));` `    ``return` `0;` `}`

Output :

`1`

Time Complexity: O(log(n)).
Auxiliary Space: O(1)

So, another challenge is “Could you do it without any loop/recursion in O(1) runtime?”

YES!!
There exists a simple and elegant O(1) solution for this too. The answer is given simply:-

```If n == 0
return 0;

If n % 9 == 0
digSum(n) = 9
Else
digSum(n) = n % 9 ```

How does the above logic works?

The logic behind this approach is :

To check if a number is divisible by 9, add the digits of the number and check if the sum is divisible by 9 or not. If yes, is the case,  the number is divisible by 9, otherwise, it’s not.

let’s take 27  i.e (2+7 = 9) hence divisible by 9.
If a number n is divisible by 9, then the sum of its digit until the sum becomes a single digit is always 9. For example,
Let, n = 2880
Sum of digits = 2 + 8 + 8 = 18: 18 = 1 + 8 = 9

Therefore,
A number can be of the form 9x or 9x + k. For the first case, the answer is always 9. For the second case, and is always k which is the remainder left.

The problem is widely known as the digit root problem.

You may find this Wikipedia article useful. -> https://en.wikipedia.org/wiki/Digital_root

Below is the implementation of the above idea :

## C++

 `#include ` `using` `namespace` `std;`   `int` `digSum(``int` `n)` `{` `    ``if` `(n == 0) ` `       ``return` `0;` `    ``return` `(n % 9 == 0) ? 9 : (n % 9);` `}`   `// Driver program to test the above function` `int` `main()` `{` `    ``int` `n = 9999;` `    ``cout<

## Java

 `import` `java.io.*;`   `class` `GFG {`   `    ``static` `int` `digSum(``int` `n)` `    ``{` `        ``if` `(n == ``0``) ` `        ``return` `0``;` `        ``return` `(n % ``9` `== ``0``) ? ``9` `: (n % ``9``);` `    ``}` `    `  `    ``// Driver program to test the above function` `    ``public` `static` `void` `main (String[] args)` `    ``{` `        ``int` `n = ``9999``;` `        ``System.out.println(digSum(n));` `    ``}` `}`   `// This code is contributed by anuj_67.`

## Python3

 `def` `digSum(n):`   `    ``if` `(n ``=``=` `0``):` `        ``return` `0` `    ``if` `(n ``%` `9` `=``=` `0``):` `        ``return` `9` `    ``else``:` `       ``return` `(n ``%` `9``)`   `# Driver program to test the above function` `n ``=` `9999` `print``(digSum(n))`   `# This code is contributed by` `# Smitha Dinesh Semwal`

## C#

 `using` `System;`   `class` `GFG` `{` `    ``static` `int` `digSum(``int` `n)` `    ``{` `        ``if` `(n == 0) ` `        ``return` `0;` `        ``return` `(n % 9 == 0) ? 9 : (n % 9);` `    ``}` `    `  `    ``// Driver Code` `    ``public` `static` `void` `Main ()` `    ``{` `        ``int` `n = 9999;` `        ``Console.Write(digSum(n));` `    `  `    ``}` `}`   `// This code is contributed by aj_36`

## PHP

 ``

## Javascript

 ``

Output:

`9`

Time Complexity: O(1)

Auxiliary Space: O(1)

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