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/ |
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