# Divisibility Equivalences

The following four sentences are equivalent. That is, they are true at the same time, and false at the same time:

The number
$\,n\,$ is divisible by $\,k\,$.

The number
$\,n\,$ is a multiple of $\,k\,$.

The number
$\,k\,$ is a factor of $\,n\,$.

The number
$\,k\,$ goes into $\,n\,$ evenly.

## Examples

‘$\,\,m\,$ is divisible by $\,j\,\,$’

‘$\,\,j\,$ goes into $\,m\,$ evenly ’

‘$\,\,n\,$ is a multiple of $\,k\,\,$’

‘$\,\,n\,$ is a factor of $\,k\,\,$’