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The definition of a Prime number is a natural number that has exactly two distinct natural number divisors. And the definition of a composite number is a natural number that has more than two finite, distinct natural number divisors.

The number one has just one natural number divisor (1), thus it doesn't fit in either category. Zero has an infinite number of natural number divisors, thus it doesn't either.

But why is it important for 1 not to be a prime number? It's not just a matter of nitpicking. If 1 is not a prime number, then any composite number (such as 12) can be written as a product of primes in only one way (here, 2*2*3), not counting different orders. However, if 1 were a prime number, there would be infinitely many ways! We could write 12 for example, as 2*2*3, or 1*2*2*3, or 1*1*1*1*1*2*2*3. Having only one way to write a number as a product of primes is very useful when doing math.

The Unique-Prime-Factorization Theorem is so useful, that it is also called the Fundamental Theorem of Arithmetic.

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โˆ™ 2017-02-24 04:50:00
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Q: Why are zero and one neither prime nor composite?
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Related questions

Is zero a prime a or composite?

Zero is neither (anyone can type a random answer you know) But zero is neither prime nor composite


Are there any numbers that are neither composite or prime?

Zero and one are neither composite nor prime.


Why is zero said to be a composite number?

Zero is neither composite nor prime.


Why is zero and one not considered prime neither composite?

Both zero and one are considered neither prime nor composite.


If zero is not prime or composite what is it?

There is no name for numbers which are neither prime nor composite.


Is 0 prime or composite?

zero is not prime or compositeIt is neither prime nor composite. See the link.


Is 0 a prime or conpositve?

Zero is neither prime nor composite.


Is zero a prime composite or a Neither?

0 is neither a prime nor a composite number.


Which are the numbers that are neither prime nor composite?

Zero and one.


What is neither a prime nor a composite number?

It is 1 that is neither a prime or a composite number The number 1 is neither prime nor composite.


Why is zero neither a prime nor composite number?

it's zero, not always counted as a number


Is 0 a composite?

No. Zero isn't a number. It's a placeholder. Therefore, it can be neither composite nor prime.


What two numbers are neither prime nor composite?

0 and 1 are neither prime nor composite.


Is zero prime composite or neither?

is a composite number. A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite.


Is 0 prime composite or neither?

0 is neither prime nor composite.


Is 1 a prime composite or neither?

It is neither prime nor composite number.


What is ONE composite or prime OR NEITHER?

ANSWER: One is neither prime nor composite.


Are there any numbers that are neither prime nor composite Explain?

The number 1 is neither composite nor prime.


Is the number 0 neither prime nor composite?

Zero is composite because it has all the real numbers as factors.


Which number are neither prime or composite?

0 and 1 are neither prime nor composite.


Why is 1 niether prime nor composite?

Why is 1 neither prime nor composite


Why is zero neither prime nor composite?

0 has every number as a factor. A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite.


Is one a prime composite or neither?

The number 1 is neither a prime nor a composite number.


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No, it is neither prime nor composite.


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Zero and one are neither prime nor composite, every other positive integer is one or the other.