audio read-through 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

Question: Compare the two sentences, and decide if they are equivalent, or not equivalent:

‘$\,\,m\,$ is divisible by $\,j\,\,$’

‘$\,\,j\,$ goes into $\,m\,$ evenly ’
Answer: equivalent
Question: Compare the two sentences, and decide if they are equivalent, or not equivalent:

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

‘$\,\,n\,$ is a factor of $\,k\,\,$’
Answer: not equivalent

Practice

equivalent
not equivalent