# Talk:Divisor

Here's another perfect example of a topic that could benefit from a plainer-language, if inexact, definition given first (and billed as "rough" or "inexact")--followed by the more precise, but harder-to-understand, definition. --Larry Sanger 17:47, 31 March 2007 (CDT)

For example (I'm not going to actually edit the article--this no doubt needs worthsmithing):

- A
**divisor**of a number, roughly speaking, "goes into" the number evenly, with nothing left over (no remainder). For example, 2 is a divisor of 4, because 2 goes into 4 two times, with nothing left over. But 2 is a not a divisor of 5, because 2 goes in 5 2.5 times.

- More exactly, given two numbers
*d*and*a,**d*is a divisor of*a*if, and only if,*a*divided by*d*equals an integer, that is, a number without fractions. So if*d*= 5 and*a*= 15, then*d*/*a*= 3, and so*d*is a divisor of*a*.

- Even more exactly and formally, given two integers
*d*and*a*, where*d*is nonzero, d is said to**divide a**, or*d*is said to be a**divisor**of*a*, if and only if there is an integer*k*such that*dk = a*. For example, 3 divides 6 because 3*2 = 6. Here 3 and 6 play the roles of*d*and*a*, while 2 plays the role of*k*. Though any number divides itself (as does its negative), it is said not to be a*proper divisor*. The number 0 is not considered to be a divisor of*any*integer.

Again, what I'm aiming at here is an explanation for people *who don't already know what "divisor" means.* Anyone who doesn't know what "divisor" means won't be able to understand the first paragraph of the article at present, which we should be able to agree is a problem.
---Larry Sanger 09:53, 3 April 2007 (CDT)-Larry Sanger 09:53, 3 April 2007 (CDT)

- I agree with the above, as does at least one other person, see my talk page. I'm all for anyone putting that stuff in at top of article asap. I will be rather busy elsewhere till 17th.Rich 17:11, 3 April 2007 (CDT)

## "proper divisors" comment

1 and -1 might be proper divisors, contrary to the current version. I think they're called trivial divisors instead. My evidence: The statement "6 is perfect because it is the sum of its proper divisors 1, 2, and 3" is *everywhere*.Rich 20:09, 31 March 2007 (CDT)

- I'll fix it. Thanks. Greg Woodhouse 20:21, 31 March 2007 (CDT)

- Man I'm over the hill! By my quote about 6 above negative numbers like -1 or -3 can't be proper divisors of 6. Sorry.Rich 12:37, 2 April 2007 (CDT)

## Further Reading

"Fearless Symmetry" is certainly a fascinating read, but really out of place in this article. (It's an introduction to the ideas behind the proof of Fermat's last theorem for non-specialists.) I was a bit, well, ebulient, in placing it here. I'll probably use it elsewhere, such as in an article on reciprocity laws. Greg Woodhouse 13:22, 2 April 2007 (CDT)