A repunit is a number consisting only of the digit 1, such as 111 and 11111. Find the number of digits in the smallest repunit divisible by 21 and 9.

 Mar 2, 2021

to do this, all we have to know is the divisible by 7 trick and the divisible by 9 trick. the divisible by 7 trick is where you take away the last digit then multiply it by two, then subtract that number from the original number, and repeat. the divisible by 9 trick is if the digits sum up to a mulitple of 9. now, you can just go with trial and error, and the lowest repunit divisible by both 21 and 9 is 111,111,111,111,111,111, which contains $\boxed{18}$ digits.

 Mar 2, 2021
edited by SparklingWater2  Mar 2, 2021

21 Online Users