• 0

One's divisibility

Question

Posted · Report post

Find the smallest number consisting of only "1"-s,

which would be divisible by "333...3" (one hundred "3"-s.)

(Decimal system.)

0

Share this post


Link to post
Share on other sites

2 answers to this question

  • 0

Posted · Report post

3333....3 is 3*1111....1


The number consisting of only ones must be a multiple of 3 and 1111...1. For it to be a multiple of 111....1, it must be a multiple of 100 1's long. The first multiple of 100 divisible by 3 is 300. So, the number is 111...1 with 300 1's.
1

Share this post


Link to post
Share on other sites
  • 0

Posted (edited) · Report post

3333....3 is 3*1111....1

The number consisting of only ones must be a multiple of 3 and 1111...1. For it to be a multiple of 111....1, it must be a multiple of 100 1's long. The first multiple of 100 divisible by 3 is 300. So, the number is 111...1 with 300 1's.

That's the number I was looking for!

Edited by Prime
0

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!


Register a new account

Sign in

Already have an account? Sign in here.


Sign In Now

  • Recently Browsing   0 members

    No registered users viewing this page.