composite and prime refresh

Even Number

An integer that yields a remainder of $0$ when divided by $2$, expressible in the form $2k$ where $k$ is an integer.

Odd Number

An integer that leaves a remainder of $1$ when divided by $2$, expressible in the form $2k + 1$ where $k$ is an integer.

Prime Number

A positive integer greater than $1$ that has exactly two distinct positive divisors: $1$ and itself.

Composite Number

A positive integer greater than $1$ that has three or more distinct positive factors.

The only even prime number

$$2$$

Why $1$ is classified as neither prime nor composite

It has only one unique positive factor ($1$), so it fails the requirement of having exactly two distinct factors as well as having three or more factors.

Smallest positive composite number

$$4$$

Classification of $0$ as even or odd

An even number, because dividing $0$ by $2$ leaves a remainder of $0$, satisfying the equation $0 = 2 \times 0$.