Repeated sum of Number's digits in JavaScript

We are required to write a JavaScript function that recursively sums up the digits of a number until it reduces to a single digit number.

We are required to do so without converting the number to String or any other data type.

How It Works

The algorithm uses two functions:

• sumDigit(): Recursively extracts and sums all digits of a number
• sumRepeatedly(): Repeatedly calls sumDigit() until result is a single digit

Example

Let's implement the solution step by step:

const num = 546767643;

const sumDigit = (num, sum = 0) => {
    if(num){
        return sumDigit(Math.floor(num / 10), sum + (num % 10));
    }
    return sum;
};

const sumRepeatedly = num => {
    while(num > 9){
        num = sumDigit(num);
    };
    return num;
};

console.log("Original number:", num);
console.log("Final result:", sumRepeatedly(num));

Original number: 546767643
Final result: 3

Step-by-Step Breakdown

Let's trace how 546767643 reduces to 3:

const traceReduction = (num) => {
    console.log("Starting with:", num);
    
    while(num > 9) {
        const digitSum = sumDigit(num);
        console.log(`Sum of digits: ${digitSum}`);
        num = digitSum;
    }
    
    console.log("Final single digit:", num);
    return num;
};

const sumDigit = (num, sum = 0) => {
    if(num){
        return sumDigit(Math.floor(num / 10), sum + (num % 10));
    }
    return sum;
};

traceReduction(546767643);

Starting with: 546767643
Sum of digits: 57
Sum of digits: 12
Sum of digits: 3
Final single digit: 3

Alternative Approach Using Math Only

Here's a more direct mathematical approach:

const digitalRoot = (num) => {
    // Handle zero case
    if (num === 0) return 0;
    
    // Mathematical formula for digital root
    return 1 + (num - 1) % 9;
};

console.log("Using formula - 546767643:", digitalRoot(546767643));
console.log("Using formula - 999:", digitalRoot(999));
console.log("Using formula - 12:", digitalRoot(12));

Using formula - 546767643: 3
Using formula - 999: 9
Using formula - 12: 3

Comparison

Conclusion

Both approaches solve the repeated digit sum problem without string conversion. The recursive method shows the step-by-step process, while the mathematical formula provides instant results using the digital root property.