Does Divisibility by 4 always work?

Date: 6/17/96 at 10:7:36
From: Anonymous
Subject: Divisibility by 4 - does it always work?

Dear Dr. Math:

I just read your web page on division tips. I have a question 
regarding the divisibility by 4 rule. Your rule says that if the last 
two digits in the number have a factor of four, the entire number is 
divisible by 4. In your second example, this makes sense, but in your 
first example the rule doesn't seem to apply. One hundred IS divisible 
by 4 but I don't how 4 / 00 gets a quotient of 25. Am I missing 
something?

Please write soon

Jessica Javor

Date: 6/17/96 at 17:30:0
From: Doctor Ethan
Subject: Re: Divisibility by 4 - does it always work?

Dear Jessica,

I am glad you are using that page, and yes, they all always work.

I will explain 4 a little more for you.

The idea is that if the last two digits are divisible by 4, then the
whole number will be.  This trick doesn't tell you anything about
what the answer will be when you do the division - it just tells you
whether or not you will have a remainder.

Let's look at 100.  The trick says to look at the last two digits.
As you pointed out they are 00.   Is zero divisible by 4?

Remember, we need to look at 00 / 4  not 4 / 00.

and 00 / 4 = 0  

Even though the answer is 0, it is still evenly divisible, so the 
trick works for all numbers.

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