+0  
 
-1
56
13
avatar+-291 

What is the least four-digit positive integer, with all different digits, that is divisible by each of its digits?

 Mar 27, 2020
 #1
avatar
0

I am not postive but maybe 102?

 Mar 27, 2020
 #4
avatar+1956 
+1

Sorry I am not CPhill, but I will help :D

 

Start with 0, and go up to 9999.

 

0 divided by anything can't be a number, so 0 is not the answer.

Every whole number is divisible by 1.

2 should be in the hundreds place to make a small number.

MAKE SURE THE NUMBER IS EVEN.

You can put a 3 in the tens place, but you cannot use any other odd numbers.

We can't use 4, since 4 is not divisible by 3, or 5.

6 is the next number that works

 

Hence, 1236 is the smallest number divisible by its digits.

 

Hope this helped!

 Mar 27, 2020
edited by CalTheGreat  Mar 27, 2020
 #9
avatar
+1

It is = 1,236

 Mar 27, 2020
 #12
avatar+111321 
0

Good work, Cal   !!!

 

I believe   that you  are correct    !!!!!

 

That was a tough one......

 

cool  cool cool

 Mar 27, 2020
edited by CPhill  Mar 27, 2020
 #13
avatar+1956 
+1

Yeah! I know this 'cause I got it wrong before lol

 

Thanks, Chris!

CalTheGreat  Mar 27, 2020

16 Online Users

avatar
avatar