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1 and 0: Prime or Composite?


Date: 10/06/97 at 10:35:55
From: Christy
Subject: The number 1 and zero

Is the number  one a prime or a composite number? Why? (Please 
put your answer in a form that a sixth grader can understand.)

What is the number zero? Prime or composite? Why?


Date: 10/06/97 at 12:47:29
From: Doctor Rob
Subject: Re: The number 1 and zero

One is neither a prime nor a composite number. A prime number is one 
with exactly two positive divisors, itself and one. One has only one 
positive divisor. It cannot be written as a product of two factors, 
neither of which is itself, so one is also not composite. It falls 
in a class of numbers called units. These are the numbers whose 
reciprocals are also whole numbers.

Zero is not a prime or a composite number either. Zero has an infinite 
number of divisors (any nonzero whole number divides zero). It cannot 
be written as a product of two factors, neither of which is itself, so 
zero is also not composite. It falls in a class of numbers called 
zero-divisors. These are numbers such that, when multiplied by some 
nonzero number, the product is zero.

The most important fact of multiplication of integers is called the
Fundamental Theorem of Arithmetic. It says that every whole number
greater than one can be written *uniquely* (except for their order) as
the product of prime numbers. This is so important that we tailor our
idea of what a prime number is to make it true. If 1 were a prime
number, this would be false, since, for example,

   7 = 1*7 = 1*1*7 = 1*1*1*7 = ...,

and the uniqueness would fail.

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
Elementary Number Sense/About Numbers
Elementary Prime Numbers
Middle School Number Sense/About Numbers
Middle School Prime Numbers

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