Given a number ‘n’, find the smallest number ‘p’ such that if we multiply all digits of ‘p’, we get ‘n’. The result ‘p’ should have minimum two digits.
Input: n = 36 Output: p = 49 // Note that 4*9 = 36 and 49 is the smallest such number Input: n = 100 Output: p = 455 // Note that 4*5*5 = 100 and 455 is the smallest such number Input: n = 1 Output:p = 11 // Note that 1*1 = 1 Input: n = 13 Output: Not Possible
For a given n, following are the two cases to be considered.
Case 1: n < 10 When n is smaller than 10, the output is always n+10. For example for n = 7, the output is 17. For n = 9, output is 19.
Case 2: n >= 10 Find all factors of n which are between 2 and 9 (both inclusive). The idea is to start searching from 9 so that the number of digits in the result is minimized. For example, 9 is preferred over 33 and 8 is preferred over 24.
Store all found factors in an array. The array would contain digits in non-increasing order, so finally print the array in reverse order.
Following is the implementation of above concept.
17 49 Not possible 455
This article is contributed by Ashish Bansal. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.
- Find smallest number with given number of digits and sum of digits under given constraints
- Find smallest possible Number from a given large Number with same count of digits
- Find smallest number with given number of digits and sum of digits
- Find the kth smallest number with sum of digits as m
- Find the smallest number whose sum of digits is N
- Find the smallest positive number which can not be represented by given digits
- Smallest number to multiply to convert floating point to natural
- Smallest number by rearranging digits of a given number
- Immediate smallest number after re-arranging the digits of a given number
- Smallest number with given sum of digits and sum of square of digits
- Get the kth smallest number using the digits of the given number
- Smallest odd number with even sum of digits from the given number N
- Smallest even digits number not less than N
- Smallest Even number with N digits
- Smallest odd digits number not less than N
- Smallest odd number with N digits
- Smallest number whose square has N digits
- Smallest number with sum of digits as N and divisible by 10^N
- Smallest number with at least n digits in factorial
- Smallest number whose sum of digits is square of N