Subject: Term definitions
A 7th grade algebra student would like the definition of the following two terms:

proper factor perfect number



Proper factor: usually we mean a factor other than the number itself. For example, 12 has the factors 1, 2, 3, 4, 6, and 12; 1, 2, 3, 4, and 6 are proper factors. I say usually because sometimes people exclude the number 1 also.

We use this concept analogously when we talk about sets and proper subsets - a proper subset is non-empty and does not have all the elements of the original set. For example, the proper subsets of the set {a, b, c} are the subsets {a}, {b}, {c}, {a,b}, {a,c} and {b,c}.

Perfect number: when you sum the proper divisors of a number and they add to the number itself, the number is said to be perfect. For example, the proper divisors of 6 are 1, 2 and 3 and 1+2+3 = 6. 28 is perfect as 1+2+4+7+14 = 28. You might try to find the next perfect number but I'll warn you it is almost 500. An interesting mathematical question is whether there are any odd perfect numbers. No one knows the answer.


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