Difference between revisions of "Proper divisor"

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A '''proper divisor''' of a [[positive integer]] <math>n</math> is any [[divisor]] of <math>n</math> other than <math>n</math> itself.  Thus, [[prime number]]s have exactly one proper divisor, 1, and every other number has at least two proper divisors.
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A '''proper divisor''' of a [[positive integer]] <math>n</math> is any [[divisor]] of <math>n</math> other than <math>n</math> itself.  Thus <math>1</math> has no proper divisors, [[prime number]]s have exactly one proper divisor <math>1</math>, and all other positive integers have at least two proper divisors.
  
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== See Also ==
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*[[Deficient number]]
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*[[Abundant number]]
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*[[Perfect number]]
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*[[2017 USAJMO Problems/Problem 4]]
 
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Latest revision as of 16:27, 10 May 2021

A proper divisor of a positive integer $n$ is any divisor of $n$ other than $n$ itself. Thus $1$ has no proper divisors, prime numbers have exactly one proper divisor $1$, and all other positive integers have at least two proper divisors.

See Also

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