urgent..cat and mouse

• September 25th 2008, 09:50 AM
anand chhetri
urgent..cat and mouse
Some cats got together and decided to kill mice numbering 999919.Each cat kills equal no.of mice and each cat kills more no.of mice than there were cats.Then what is the number of cats?
• September 25th 2008, 10:23 AM
Laurent
You may find useful to know that $999919=991\times 1009$ where both factors are prime...
• September 27th 2008, 11:53 AM
narbe
Dear Friend,
Laurent gives the accurate answer. As an extra explanation we can say :

n(n+b)=999919
where n is number of cats, and b is the difference between number of mice caught by cats and number of cats.

As Laurent said :

(991)(991 + b ) = 999919
b = 18

(991)(991 + 18 ) 999919 (Wink)