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Table of divisors

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Table of divisors
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The tables below list all of the divisors of the numbers 1 to 1000.

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Plot of the number of divisors of integers from 1 to 1000. Highly composite numbers are labelled in bold and superior highly composite numbers are starred. In the SVG file, hover over a bar to see its statistics.

A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21).

If m is a divisor of n, then so is m. The tables below only list positive divisors.

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Key to the tables

  • d(n) is the number of the positive divisors of n, including 1 and n itself
  • σ(n) is the sum of the positive divisors of n, including 1 and n itself
  • s(n) is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n)  n
  • a deficient number is greater than the sum of its proper divisors; that is, s(n) < n
  • a perfect number equals the sum of its proper divisors; that is, s(n) = n
  • an abundant number is lesser than the sum of its proper divisors; that is, s(n) > n
  • a highly abundant number has a sum of positive divisors that is greater than any lesser number; that is, σ(n) > σ(m) for every positive integer m < n. Counterintuitively, the first seven highly abundant numbers (as well as the ninth) are not abundant numbers.
  • a prime number has only 1 and itself as divisors; that is, d(n) = 2
  • a composite number has more than just 1 and itself as divisors; that is, d(n) > 2
  • a highly composite number has a number of positive divisors that is greater than any lesser number; that is, d(n) > d(m) for every positive integer m < n. Counterintuitively, the first two highly composite numbers are not composite numbers.
  • a superior highly composite number has a ratio between its number of divisors and itself raised to some positive power that equals or is greater than any other number; that is, there exists some ε such that for every other positive integer m
  • a primitive abundant number is an abundant number whose proper divisors are all deficient numbers
  • a weird number is a number that is abundant but not semiperfect; that is, no subset of the proper divisors of n sum to n
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1 to 100

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101 to 200

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201 to 300

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301 to 400

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401 to 500

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501 to 600

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601 to 700

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701 to 800

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801 to 900

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901 to 1000

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Sortable 1-1000

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See also

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