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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

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    $\begingroup$ Maybe 'exactly' could be used. Many students use equally and evenly interchangeably $\endgroup$ – Karl May 30 '15 at 19:09
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    $\begingroup$ 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.) $\endgroup$ – Benjamin Dickman May 30 '15 at 19:25
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    $\begingroup$ How about "with no remainder"? $\endgroup$ – JoeTaxpayer May 30 '15 at 20:02
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    $\begingroup$ 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.) $\endgroup$ – Daniel Hast May 31 '15 at 5:49
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    $\begingroup$ 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". $\endgroup$ – Jared May 31 '15 at 7:17
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Make it clear to your students to begin with that when it comes to divisibility, we are only ever interested in whole number divisibility. Otherwise, of course any non-zero number 'divides' any other number! (I assume you're working with the reals).

So it will then suffice to simply say

2 divides 14

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