Table of divisors

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

A divisor of an integer "n" is an integer "m", say, 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 21/3 = 7 (and 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.

Key to the tables

*"d"("n") is the number of positive divisors of "n", including 1 and "n" itself
*σ("n") is the sum of all the positive divisors of "n", including 1 and "n" itself
*"s"("n") is the sum of the proper divisors of "n", which does not include "n" itself; that is, "s"("n") = σ("n") − "n"
*a perfect number equals the sum of its proper divisors; that is, "s"("n") = "n"; the only perfect numbers between 1 and 1000 are 6, 28 and 496
*amicable numbers and sociable numbers are numbers where the sum of their proper divisors form a cycle; the only examples below 1000 are 220 and 284
*a deficient number is greater than the sum of its proper divisors; that is, "s"("n") < "n"
*an abundant number is less than the sum of its proper divisors; that is, "s"("n") > "n"
*a prime number has only 1 and itself as divisors; that is, "d"("n") = 2. Prime numbers are always deficient as "s"("n")=1

Divisors of the numbers 1 to 100

Divisors of the numbers 301 to 400

Divisors of the numbers 601 to 700

Divisors of the numbers 901 to 1000

ee also

*Table of prime factors for numbers 1 to 1000