Divisible...

Date: 8/27/96 at 21:29:2
From: Anonymous
Subject: Divisible...

Which of these numbers are divisible by {5, 8, 9}: 
{14, 73, 2, 21, 25, 84, 34, 52, 13}? 

Date: 8/28/96 at 3:28:55
From: Doctor Mike
Subject: Re: Divisible...

Hello,

Since 14 is first let's look at it now. Divide 14 by each of 
5, 8, and 9 and you get 2.8, 1.75 and 1.55555555555.... Notice that 
none of these is a whole number. They all have fractional parts. That 
means that 14 is NOT divisible by 5 or 8 or 9. 

You get the same result for 73 and 2 and 21. 

However, 25 is divisible by 5 since 25 divided by 5 is the whole 
number 5.  None of the rest is divisible by 5 or 8 or 9.  
  
Another way to look at this that sometimes is handy is to list all the 
numbers divisible by, say 5, and compare to your list.
  
Divisible by 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, etc.
Divisible by 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, etc.
Divisible by 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, etc.
  
What I have done here is to write out each of the numbers 5,8,9 
multiplied by 1, 2, 3, 4, 5, 6, etc.  As you can see, the only number 
on your list that appears in any of those 3 lines is 25, so this is 
another way to see that only 25 fills your requirement.
  
I hope this is the help you need.  

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/