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

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Identifying Inequalities as True or False

(an even number, please)