JavaScript: Smallest number whose digits multiply to a number

JavaScript Math: Exercise-113 with Solution

Smallest Number from Digit Product

Write a JavaScript program to calculate the smallest number whose digits multiply into a given number.

Example:
let n =100

Test Data:
(100) -> 455
(120) -> 358
(16) -> 28
(129) -> 0

Sample Solution:

JavaScript Code:

/**
 * Function to find the smallest number whose digits multiply to the given number.
 * @param {number} n - The given number.
 * @returns {number} - The smallest number whose digits multiply to the given number.
 */
function test(n) {
    if (n < 10) return n; // If n is less than 10, return n itself
    data = []; // Array to store all occurrences of digits
    for (i = 9; i > 1; i--) {
        // Store all occurrences of current digit in data 
        // if current digit divides n.
        while (n % i === 0) {
            n = n / i;
            data.push(i);
        }
    }

    if (n != 1) return 0; // If n is not 1, it means it contains a prime number greater than 9, so return 0
    result = 0; // Initialize result to store the smallest number whose digits multiply to n
    for (i = data.length - 1; i >= 0; i--) {
        result = result * 10 + data[i]; // Build the result number from the array data
        if (result > Number.MAX_VALUE) return 0; // If result exceeds the maximum value for a number, return 0
    }
    return result; // Return the smallest number whose digits multiply to n
}

// Test cases
n = 100;
console.log("n = " + n);
console.log("Smallest number whose digits multiply to the said number: " + test(n));
n = 120;
console.log("n = " + n);
console.log("Smallest number whose digits multiply to the said number: " + test(n));
n = 16;
console.log("n = " + n);
console.log("Smallest number whose digits multiply to the said number: " + test(n));
n = 129;
console.log("n = " + n);
console.log("Smallest number whose digits multiply to the said number: " + test(n));

Output:

n = 100
Smallest number whose digits multiply to the said number: 455
n = 120
Smallest number whose digits multiply to the said number: 358
n = 16
Smallest number whose digits multiply to the said number: 28
n = 129
Smallest number whose digits multiply to the said number: 0

Flowchart:

Live Demo:

See the Pen javascript-math-exercise-113 by w3resource (@w3resource) on CodePen.

For more Practice: Solve these Related Problems:

• Write a JavaScript function that finds the smallest number whose digits multiply to a given number by factorizing the input.
• Write a JavaScript function that decomposes a number into factors and arranges them to form the smallest possible integer.
• Write a JavaScript function that handles cases where the digit product cannot form a valid number and returns an error.
• Write a JavaScript function that uses a greedy algorithm to construct the minimal number from the factors of the input product.

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