All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Find All Numbers (Posted on 2006-07-25) Difficulty: 3 of 5
Find all four–digit numbers in which the product of the digits is equal to the sum of the digits, and the number itself is divisible by the sum of its digits.

No Solution Yet Submitted by Ravi Raja    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 2 of 7 |

4112 and -4112.

As the product is equal to the sum, the digits must be 1,1,2,4. No other set of digits could offer a solution.  The following is the list of positive numbers where the product  and sum of the digits are equal: 1124, 1142, 1214, 1241, 1412, 1421, 2114, 2141, 2411, 4112, 4121, & 4211.  Of these the only 4112 is evenly divisible by 8.  As the problem does not require the number (only the digits) to be positive, -4112 is also valid as it is also a four-digit number divisible by the sum of its digits. 


  Posted by Dej Mar on 2006-07-25 11:52:10
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information