Given a positive integer N whose unit’s digit is 3. Find the number of 1s in the smallest repunit which is divisible by the given number N. Every number whose unit’s digit is 3 has a repunit as its multiple. A repunit is a number which has only ones. It is of the form (10n – 1)/9.
As 3 divides 111 which is the smallest repunit
multiple of the number. So the number of ones in 111 is 3.
The repunits are 1, 11, 111, 1111, …. the next repunit to x will always be x*10+1. If the remainder left by x repunit is r then remainder left by the next repunit will always be (r*10+1)%n. Since the repunit can be very large, there is no need to find the repunit number. Simply counting the number of ones will give us the answer.
So, find out the remainders of all repunit numbers until the remainder becomes 0. Once it does, then the count of iterations done to make remainder 0 will be the number of 1’s.
Below is the implementation of above approach :
- Find the smallest number whose digits multiply to a given number n
- Smallest number by rearranging digits of a given number
- Immediate smallest number after re-arranging the digits of a given number
- Get the kth smallest number using the digits of the given number
- Smallest odd digits number not less than N
- Smallest even digits number not less than N
- Find smallest number K such that K % p = 0 and q % K = 0
- Smallest odd number with N digits
- Smallest Even number with N digits
- Smallest K digit number divisible by X
- Smallest triangular number larger than p
- Largest and smallest digit of a number
- Find smallest permutation of given number
- Find smallest number n such that n XOR n+1 equals to given k.
- Smallest N digit number which is a multiple of 5
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.