# Correct term to say that a number divides another number "evenly"?

This is something that has continued to bother me in general, and recently I had multiple occasions where saying something like "2 divides 14 evenly" has confused students, They expected the result to be an even number, not $7$. I can't seem to find the concise word/wording for saying that a number divides another without a remainder? I would like to start using this instead of "evenly" for my students' benefit

• Maybe 'exactly' could be used. Many students use equally and evenly interchangeably
– Karl
May 30, 2015 at 19:09
• 2 divides 14 with remainder 0; 2 is a divisor of 14; 2 is a factor of 14; 14 is a multiple of 2; 14 divided by 2 is a whole number. Etc. (Or you could explain precisely what you mean by "evenly" in this context.) May 30, 2015 at 19:25
• How about "with no remainder"? May 30, 2015 at 20:02
• I like "m is a divisor/factor of n", because this makes it clear that divisibility is a relation, not a process. (Phrases like "m divides n without remainder" could make it sound like m is actively doing something to n, rather than having some preexisting relation to n.) May 31, 2015 at 5:49
• It seems to me the problem is the commonality between the words "evenly" and "even" here. My suggestion would be "cleanly", so "2 divides 14 cleanly" (i.e. there's no mess, no remainders). Although I will say that stating things this way is confusing on the face of things--I think students would be more accustomed to "14 can be divided into 2 cleanly". May 31, 2015 at 7:17