# Which even number is not a composite number?

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The number 2 is even but it is not a composite number. This is because the number 2 is prime. If we restrict ourselves to natural numbers then 2 is the only even number that is not a composite number. On the other hand, if we allow 0 to be considered then 0 is also an even number that is not composite. In fact, 0 is considered to be neither a prime nor a composite number. Thus 0 and 2 are the only non-negative even numbers that are not composite

### Why is 2 not a composite number?

As mentioned above 2 is not a composite number because it is a prime number. This is because it has exactly two factors – 1 and itself. A composite number must have three or more factors, that is, a composite number must have a factor other than 1 or itself in order to be classified as composite. Since 2 does not have a factor other than 1 or itself, it is not a composite number.

### How is 0 an even number that is not composite?

We must first understand why 0 is an even number. An even number is defined as a number that is divisible by 2. Since the number 0 is divisible by any integer it is clearly divisible by 2. Therefore 0 is considered to be an even number.

We now explain why 0 is not composite. At first glance, it seems that 0 is composite since every number divides 0. But notice that any composite number can be written as a product of distinct prime factors. For example, 6 is composite because it can be written as the product of the primes 2 and 3. 6 = 2 \times 3. On the other hand 0 cannot be written as a product of prime factors because the product of any non-zero prime numbers will clearly be non-zero. This shows that 0 is not a composite number.

#### Why are all nonnegative even numbers other than 2 and 0 composite?

By definition, an even number is a number that has 2 as a factor. Let “N” be an even number other than 2 or 0. The number N has two obvious factors – 1 and itself. Since N is not equal to 2 and N is even, the number 2 is another distinct factor of N. Since N has at least 3 different factors – 1, 2 and N – we can conclude that it is indeed a composite number.

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