# Divisibility Calculators

A number $$n$$ is divisible by $$d$$ if and only if the remainder of the operation $$n \div d$$ is equal to zero.

Another way to say the same thing is:

$$n \space mod \space d = 0$$ (modulo calculator)
$$n \space \equiv_{d} \space 0$$
$$n \space \equiv \space 0 \space (mod \space d)$$
$$n \div d = c, c \in \mathbb{Z}$$, where $$\mathbb{Z}$$ denotes the set of integers.

Example:

• $$10 \div 5 = 2$$ (10 is divisible by 5 because 2 is an integer)

To save ourselves the effort of writing "The number $$a$$ divides $$n$$", we write: $$a|n$$.

Examples:

• $$2|10$$ is true
• $$3|7$$ is false

### Calculators

Use these calculators to figure out whether or not a given number is divisible by another one.