# 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 | + | 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. |

+ | == See Also == | ||

+ | *[[Deficient number]] | ||

+ | *[[Abundant number]] | ||

+ | *[[Perfect number]] | ||

+ | *[[2017 USAJMO Problems/Problem 4]] | ||

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## Latest revision as of 15:27, 10 May 2021

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

## See Also

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