#2847 - Smallest Number With Given Digit Product

Medium • View on LeetCode • View on GitHub

Problem Description

Given a positive integer n, return a string representing the smallest positive integer such that the product of its digits is equal to n, or "-1" if no such number exists.

Solution

/**
 * @param {number} n
 * @return {string}
 */
var smallestNumber = function(n) {
  if (n < 10) return n.toString();

  const digits = [];
  let remaining = BigInt(n);
  for (let digit = 9; digit > 1 && remaining > 1n; digit--) {
    const bigDigit = BigInt(digit);
    while (remaining % bigDigit === 0n) {
      digits.push(digit);
      remaining /= bigDigit;
    }
  }

  if (remaining !== 1n) return '-1';

  return digits.reverse().join('');
};