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# Digital Root of a given large number using Recursion

• Difficulty Level : Hard
• Last Updated : 20 Dec, 2022

Given a large number num in the form of string with length as N, the task is to find its digital root

The digital root of a positive integer is found by summing the digits of the integer. If the resulting value is a single digit then that digit is the digital root. If the resulting value contains two or more digits, those digits are summed and the process is repeated. This is continued as long as necessary to obtain a single digit.

Examples:

Input: num = 675987890789756545689070986776987
Output:
Explanation:
Sum of individual digit of the above number = 212
Sum of individual digit of 212 = 5
So the Digital root is 5

Input: num = 876598758938317432685778263
Output:
Explanation:
Sum of individual digit of the above number = 155
Sum of individual digit of 155 = 11
Sum of individual digit of 11 = 2
So the Digital root is 2

Approach:

Follow the below steps to solve the problem:

• Find out all the digits of a number.
• Add all the number one by one.
• If the final sum contains more than one digit, Call the recursive function again to make it a single digit.
• The result obtained in the single-digit is the Digital Root of the number.

Below is the implementation of the above approach:

## C++

 `// C++ program to print the digital``// root of a given very large number` `#include ``using` `namespace` `std;` `// Function to convert given``// sum into string``string convertToString(``int` `sum)``{``    ``string str = ``""``;``    ``// Loop to extract digit one by one``    ``// from the given sum and concatenate``    ``// into the string``    ``while` `(sum) {``        ``// Type casting for concatenation``        ``str = str + (``char``)((sum % 10) + ``'0'``);``        ``sum = sum / 10;``    ``}``    ``// Return converted string``    ``return` `str;``}` `// Function to get individual digit``// sum from string``string GetIndividulaDigitSum(string str, ``int` `len)``{``    ``int` `sum = 0;``    ``// Loop to get individual digit sum``    ``for` `(``int` `i = 0; i < len; i++) {``        ``sum = sum + str[i] - ``'0'``;``    ``}``    ``// Function call to convert``    ``// sum into string``    ``return` `convertToString(sum);``}` `// Function to calculate the digital``// root of a very large number``int` `GetDigitalRoot(string str)``{``    ``// Base condition``    ``if` `(str.length() == 1) {``        ``return` `str - ``'0'``;``    ``}``    ``// Function call to get``    ``// individual digit sum``    ``str = GetIndividulaDigitSum(str, str.length());``    ``// Recursive function to get digital``    ``// root of a very large number``    ``return` `GetDigitalRoot(str);``}` `// Driver code``int` `main()``{``    ``string str = ``"675987890789756545689070986776987"``;` `    ``// Function call``    ``cout << GetDigitalRoot(str);``}`

## Java

 `// Java program to print the digital``// root of a given very large number``import` `java.util.*;``import` `java.io.*;``class` `GFG {` `    ``// Function to convert given``    ``// sum into String``    ``static` `String convertToString(``int` `sum)``    ``{``        ``String str = ``""``;` `        ``// Loop to extract digit one by one``        ``// from the given sum and concatenate``        ``// into the String``        ``while` `(sum > ``0``) {` `            ``// Type casting for concatenation``            ``str = str + (``char``)((sum % ``10``) + ``'0'``);``            ``sum = sum / ``10``;``        ``}` `        ``// Return converted String``        ``return` `str;``    ``}` `    ``// Function to get individual digit``    ``// sum from String``    ``static` `String GetIndividulaDigitSum(String str, ``int` `len)``    ``{``        ``int` `sum = ``0``;` `        ``// Loop to get individual digit sum``        ``for` `(``int` `i = ``0``; i < len; i++) {``            ``sum = sum + str.charAt(i) - ``'0'``;``        ``}` `        ``// Function call to convert``        ``// sum into String``        ``return` `convertToString(sum);``    ``}` `    ``// Function to calculate the digital``    ``// root of a very large number``    ``static` `int` `GetDigitalRoot(String str)``    ``{``        ``// Base condition``        ``if` `(str.length() == ``1``) {``            ``return` `str.charAt(``0``) - ``'0'``;``        ``}` `        ``// Function call to get``        ``// individual digit sum``        ``str = GetIndividulaDigitSum(str, str.length());` `        ``// Recursive function to get digital``        ``// root of a very large number``        ``return` `GetDigitalRoot(str);``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``String str = ``"675987890789756545689070986776987"``;` `        ``// Function call``        ``System.out.print(GetDigitalRoot(str));``    ``}``}` `// This code is contributed by sapnasingh4991`

## Python3

 `# Python3 program to print the digital``# root of a given very large number` `# Function to convert given``# sum into string`  `def` `convertToString(``sum``):``    ``str1 ``=` `""` `    ``# Loop to extract digit one by one``    ``# from the given sum and concatenate``    ``# into the string``    ``while` `(``sum``):` `        ``# Type casting for concatenation``        ``str1 ``=` `str1 ``+` `chr``((``sum` `%` `10``) ``+` `ord``(``'0'``))``        ``sum` `=` `sum` `/``/` `10` `    ``# Return converted string``    ``return` `str1` `# Function to get individual digit``# sum from string`  `def` `GetIndividulaDigitSum(str1, len1):``    ``sum` `=` `0``    ``# Loop to get individual digit sum``    ``for` `i ``in` `range``(len1):``        ``sum` `=` `sum` `+` `ord``(str1[i]) ``-` `ord``(``'0'``)` `    ``# Function call to convert``    ``# sum into string``    ``return` `convertToString(``sum``)` `# Function to calculate the digital``# root of a very large number`  `def` `GetDigitalRoot(str1):``    ``# Base condition``    ``if` `(``len``(str1) ``=``=` `1``):``        ``return` `ord``(str1[``0``]) ``-` `ord``(``'0'``)` `    ``# Function call to get``    ``# individual digit sum``    ``str1 ``=` `GetIndividulaDigitSum(str1, ``len``(str1))``    ``# Recursive function to get digital``    ``# root of a very large number``    ``return` `GetDigitalRoot(str1)` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``str1 ``=` `"675987890789756545689070986776987"` `    ``# Function call``    ``print``(GetDigitalRoot(str1))` `# This code is contributed by Surendra_Gangwar`

## C#

 `// C# program to print the digital``// root of a given very large number``using` `System;``class` `GFG {` `    ``// Function to convert given``    ``// sum into String``    ``static` `String convertToString(``int` `sum)``    ``{``        ``String str = ``""``;` `        ``// Loop to extract digit one by one``        ``// from the given sum and concatenate``        ``// into the String``        ``while` `(sum > 0) {``            ``// Type casting for concatenation``            ``str = str + (``char``)((sum % 10) + ``'0'``);``            ``sum = sum / 10;``        ``}` `        ``// Return converted String``        ``return` `str;``    ``}` `    ``// Function to get individual digit``    ``// sum from String``    ``static` `String GetIndividulaDigitSum(String str, ``int` `len)``    ``{``        ``int` `sum = 0;` `        ``// Loop to get individual digit sum``        ``for` `(``int` `i = 0; i < len; i++) {``            ``sum = sum + str[i] - ``'0'``;``        ``}` `        ``// Function call to convert``        ``// sum into String``        ``return` `convertToString(sum);``    ``}` `    ``// Function to calculate the digital``    ``// root of a very large number``    ``static` `int` `GetDigitalRoot(String str)``    ``{``        ``// Base condition``        ``if` `(str.Length == 1) {``            ``return` `str - ``'0'``;``        ``}` `        ``// Function call to get``        ``// individual digit sum``        ``str = GetIndividulaDigitSum(str, str.Length);` `        ``// Recursive function to get digital``        ``// root of a very large number``        ``return` `GetDigitalRoot(str);``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``String str = ``"675987890789756545689070986776987"``;` `        ``// Function call``        ``Console.Write(GetDigitalRoot(str));``    ``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output

`5`

Time Complexity: O(N), which can be computed as follows:

• O(log N) time to find the sum of digits of num first time, where N is the count of digits initially.
• O(log log N) time to find the sum of digits next time
• O(log log log N) time to find the sum of digits next time
• … and so on.

Auxiliary Space: O(1), since the sum stored in the string will not exceed 3 digits for N ≤ 105

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