# Question #0ff60

Jul 11, 2016

There's no need for a proof. The number 1 is not prime by definition.

#### Explanation:

See the very first sentence at: https://en.wikipedia.org/wiki/Prime_number

The reason we define 1 to not be prime is so that the Fundamental Theorem of Arithmetic can be stated in its simplest form. See: https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic

Also note that 1 is not composite either. It's in a special class by itself. It's often called a "unit".

Jul 14, 2016

1 has only one factor, it is therefore neither prime nor composite.

#### Explanation:

If one refers to the number of factors, then 1 is neither prime nor composite.....

"A prime number is a natural number which has only 2 factors, (1 and itself)"

A composite number is a natural number which has more than 2 factors"

As 1 has only one factor, (1), it does not meet the requirements of either prime or composite numbers.

However, it is interesting to note that a SQUARE number has an ODD number of factors. As 1 has one factor, it is a square number.

$1 \times 1 = {1}^{2} = 1$