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.