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32640 = 273517
BaseRepresentation
bin111111110000000
31122202220
413332000
52021030
6411040
7164106
oct77600
948686
1032640
1122583
1216a80
1311b1a
14bc76
159a10
hex7f80

32640 has 64 divisors (see below), whose sum is σ = 110160. Its totient is φ = 8192.

The previous prime is 32633. The next prime is 32647. The reversal of 32640 is 4623.

32640 = T51 + T52 + ... + T68.

32640 is a nontrivial binomial coefficient, being equal to C(256, 2).

It is an interprime number because it is at equal distance from previous prime (32633) and next prime (32647).

It is a tau number, because it is divible by the number of its divisors (64).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a nialpdrome in base 2 and base 8.

It is a zygodrome in base 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (32647) by changing a digit.

32640 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

In principle, a polygon with 32640 sides can be constructed with ruler and compass.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1912 + ... + 1928.

232640 is an apocalyptic number.

32640 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

32640 is the 255-th triangular number and also the 128-th hexagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 32640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (55080).

32640 is an abundant number, since it is smaller than the sum of its proper divisors (77520).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

32640 is a wasteful number, since it uses less digits than its factorization.

32640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 39 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 15.

The square root of 32640 is about 180.6654366502. The cubic root of 32640 is about 31.9582789618.

The spelling of 32640 in words is "thirty-two thousand, six hundred forty".

Divisors: 1 2 3 4 5 6 8 10 12 15 16 17 20 24 30 32 34 40 48 51 60 64 68 80 85 96 102 120 128 136 160 170 192 204 240 255 272 320 340 384 408 480 510 544 640 680 816 960 1020 1088 1360 1632 1920 2040 2176 2720 3264 4080 5440 6528 8160 10880 16320 32640