Numbers were last digit is zero, are even.

Example: 10, 20, 30, 40, etc.

Attention: Zero!

The number Zero is neither odd nor even.

$$\forall x \in \mathbb{Z}, x \neq 0$$

$$x \cdot 2 \Rightarrow \text{even number} = pairs$$

1. A pair consists of two elements.
2. Dividing a number by two, we count the number of pairs.
3. Zero elements, resulting zero pairs.

$$\forall x\in \mathbb{Z}, x \neq 0 ,$$

$$\begin{cases} x \mod 2 = 0, & \text{x $\Rightarrow$ even} \\ x \mod 2 = 1, & \text{x $\Rightarrow$ odd} \end{cases}$$

In words we say:

for any integer $\forall x \in \mathbb{Z}$,

• the number is odd, if divided to two, the rest is one.
• the number is even, if divided to two, the whole not zero, and the rest is zero.

The number Zero is neither odd nor even.

JavaScript:

var pairs=Math.floor(number/2);  
var remainder=number%2;  
if (remainder){  
    console.log("Number is ODD");
}else if (pairs && remainder === 0){
    console.log("Number is EVEN");
}else{
    console.log("Number ZERO is neither ODD nor EVEN");
};