+0  
 
+7
185
3
avatar+530 

What is the least positive integer that has only 1s and 0s as digits and is a multiple of 75?

 

I understand the answer is 148, as I found myself by multiplying 75 by even numbers until I got to 11100. 
But how would you find this quicker?

 

Thanks in advance! 

 Jul 16, 2020
 #1
avatar+2152 
+1

Hi, CentsLord.

 

I found a useful article for you :)

https://math.stackexchange.com/questions/164986/smallest-multiple-whose-digits-are-only-ones-and-zeros

 

BTW do you happen to use AoPS? I think I know you there.... what's your username?

 Jul 16, 2020
edited by CalTheGreat  Jul 16, 2020
 #2
avatar+530 
+7

Lol, clearly you're from AoPS. I can see your Avatar was created by a user... I forgot their name but they've made many avatars xD

CentsLord  Jul 16, 2020
 #3
avatar+2152 
0

Flec you mean. I am flec.

CalTheGreat  Jul 16, 2020
edited by CalTheGreat  Jul 16, 2020

16 Online Users

avatar
avatar
avatar