Divisibility rules for the numbers 2 through 10 (Is a number divisible by 2? By 3? By 4? etc.)

What does it mean for a number to be “divisible” by another number?

When we talk about the “divisibility” of a whole number, we’re just talking about the whole numbers that divide evenly into it. As an example, $5$ divides evenly into $15$ three times, since $15\div5=3$ , which means we can say that $15$ is “divisible” by $5$ .

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If we want to be technical, $15$ is divisible by $5$ because when we do the division $15\div5$ , the answer we get ( $3$ ) is a whole number. That’s the technical definition of divisibility: The result of the division must be a whole number.

Another way to say this is that we must get a remainder of $0$ . Since we often think of $0$ as “nothing,” we sometimes say that there’s no remainder when the remainder is $0$ . So a third way to say that one whole number is divisible by another is that we don’t get a remainder when we do the division.

Here’s a counterexample. Is $9$ divisible by $4$ ? If we divide $9$ by $4$ , we know $4$ goes into $9$ two times, and that gets us up to $8$ , but then we have a remainder of $1$ . In other words, because we have a remainder (other than $0$ ), our answer isn’t a whole number. We get a whole number as the answer for $8\div4$ (the answer is the whole number $2$ ), and we get a whole number as the answer for $12\div4$ (the answer is the whole number $3$ ), but we don’t get a whole number as the answer for $9\div4$ . Therefore, we can say that $9$ is not divisible by $4$ . But as we just saw, $8$ and $12$ are both divisible by $4$ .

The following list of divisibility rules are a shorthand way of determining if a particular integer is divisible by another, without actually performing the division.

Divisible by $2$ if the last digit is $0,\ 2,\ 4,\ 6,\ 8$