The tables below list all of the divisors of the numbers 1 to 1000.
A divisor of an integer n is an integer m, for which is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since = 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.
0 is excluded, given that since every number a can divide into it for a result of 0, it technically has infinitely many divisors.
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 the ratio of 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
1 to 100
nDivisorsd(n)σ(n)s(n)Notes11110deficient, highly abundant, highly composite21, 2231deficient, highly abundant, prime, highly composite, superior highly composite31, 3241deficient, highly abundant, prime41, 2, 4373deficient, highly abundant, composite, highly composite51, 5261deficient, prime61, 2, 3, 64126perfect, highly abundant, composite, highly composite, superior highly composite71, 7281deficient, prime81, 2, 4, 84157deficient, highly abundant, composite91, 3, 93134deficient, composite101, 2, 5, 104188deficient, highly abundant, composite111, 112121deficient, prime121, 2, 3, 4, 6, 1262816abundant, highly abundant, composite, highly composite, superior highly composite131, 132141deficient, prime141, 2, 7, 1442410deficient, composite151, 3, 5, 154249deficient, composite161, 2, 4, 8, 1653115deficient, highly abundant, composite171, 172181deficient, prime181, 2, 3, 6, 9, 1863921abundant, highly abundant, composite191, 192201deficient, prime201, 2, 4, 5, 10, 2064222abundant, highly abundant, composite, primitive abundantnDivisorsd(n)σ(n)s(n)Notes211, 3, 7, 2143211deficient, composite221, 2, 11, 2243614deficient, composite231, 232241deficient, prime241, 2, 3, 4, 6, 8, 12, 2486036abundant, highly abundant, composite, highly composite251, 5, 253316deficient, composite261, 2, 13, 2644216deficient, composite271, 3, 9, 2744013deficient, composite281, 2, 4, 7, 14, 2865628perfect, composite291, 292301deficient, prime301, 2, 3, 5, 6, 10, 15, 3087242abundant, highly abundant, composite311, 312321deficient, prime321, 2, 4, 8, 16, 3266331deficient, composite331, 3, 11, 3344815deficient, composite341, 2, 17, 3445420deficient, composite351, 5, 7, 3544813deficient, composite361, 2, 3, 4, 6, 9, 12, 18, 3699155abundant, highly abundant, composite, highly composite371, 372381deficient, prime381, 2, 19, 3846022deficient, composite391, 3, 13, 3945617deficient, composite401, 2, 4, 5, 8, 10, 20, 4089050abundant, compositenDivisorsd(n)σ(n)s(n)Notes411, 412421deficient, prime421, 2, 3, 6, 7, 14, 21, 4289654abundant, highly abundant, composite431, 432441deficient, prime441, 2, 4, 11, 22, 4468440deficient, composite451, 3, 5, 9, 15, 4567833deficient, composite461, 2, 23, 4647226deficient, composite471, 472481deficient, prime481, 2, 3, 4, 6, 8, 12, 16, 24, 481012476abundant, highly abundant, composite, highly composite491, 7, 493578deficient, composite501, 2, 5, 10, 25, 5069343deficient, composite511, 3, 17, 5147221deficient, composite521, 2, 4, 13, 26, 5269846deficient, composite531, 532541deficient, prime541, 2, 3, 6, 9, 18, 27, 54812066abundant, composite551, 5, 11, 5547217deficient, composite561, 2, 4, 7, 8, 14, 28, 56812064abundant, composite571, 3, 19, 5748023deficient, composite581, 2, 29, 5849032deficient, composite591, 592601deficient, prime601, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 6012168108abundant, highly abundant, composite, highly composite, superior highly compositenDivisorsd(n)σ(n)s(n)Notes611, 612621deficient, prime621, 2, 31, 6249634deficient, composite631, 3, 7, 9, 21, 63610441deficient, composite641, 2, 4, 8, 16, 32, 64712763deficient, composite651, 5, 13, 6548419deficient, composite661, 2, 3, 6, 11, 22, 33, 66814478abundant, composite671, 672681deficient, prime681, 2, 4, 17, 34, 68612658deficient, composite691, 3, 23, 6949627deficient, composite701, 2, 5, 7, 10, 14, 35, 70814474abundant, composite, primitive abundant, weird711, 712721deficient, prime721, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 7212195123abundant, highly abundant, composite731, 732741deficient, prime741, 2, 37, 74411440deficient, composite751, 3, 5, 15, 25, 75612449deficient, composite761, 2, 4, 19, 38, 76614064deficient, composite771, 7, 11, 7749619deficient, composite781, 2, 3, 6, 13, 26, 39, 78816890abundant, composite791, 792801deficient, prime801, 2, 4, 5, 8, 10, 16, 20, 40, 8010186106abundant, compositenDivisorsd(n)σ(n)s(n)Notes811, 3, 9, 27, 81512140deficient, composite821, 2, 41, 82412644deficient, composite831, 832841deficient, prime841, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 8412224140abundant, highly abundant, composite851, 5, 17, 85410823deficient, composite861, 2, 43, 86413246deficient, composite871, 3, 29, 87412033deficient, composite881, 2, 4, 8, 11, 22, 44, 88818092abundant, composite, primitive abundant891, 892901deficient, prime901, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 9012234144abundant, highly abundant, composite911, 7, 13, 91411221deficient, composite921, 2, 4, 23, 46, 92616876deficient, composite931, 3, 31, 93412835deficient, composite941, 2, 47, 94414450deficient, composite951, 5, 19, 95412025deficient, composite961, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 9612252156abundant, highly abundant, composite971, 972981deficient, prime981, 2, 7, 14, 49, 98617173deficient, composite991, 3, 9, 11, 33, 99615657deficient, composite1001, 2, 4, 5, 10, 20, 25, 50, 1009217117abundant, composite
101 to 200