Is Zero a Multiple of Every Number?

Date: 07/06/2002 at 12:35:48
From: Prabha Sethy
Subject: Factors and multiples

Is zero a multiple of every number?

I teach math to children and I find that some books state that zero 
is a multiple of every number, whereas some books state that zero is 
not a multiple of every number. 

I want to know the correct answer so that I can teach the children 
the correct fact.

Date: 07/06/2002 at 12:58:58
From: Doctor Paul
Subject: Re: Factors and multiples

Let x and y be integers.  Then x is a multiple of y if there exists 
another integer z such that x = y*z.

That is the definition.  Now let x = zero and let y be an arbitrary 
integer.  Can we find an integer z such that 0 = y*z?  I think 
you'll see that choosing z = zero will do the trick every time.  So 
zero is a multiple of every integer.

I hope this helps.  Please write back if you'd like to talk about 
this some more.

- Doctor Paul, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 07/06/2002 at 13:35:46
From: Prabha Sethy
Subject: Thank you (Factors and multiples)

Thanks so much for a quick response.  This has helped clear my 
doubt.