51840 has 80 divisors (see below), whose sum is σ = 185130. Its totient is φ = 13824.

The previous prime is 51839. The next prime is 51853. The reversal of 51840 is 4815.

It is a Jordan-Polya number, since it can be written as 6! ⋅ (3!)^{2} ⋅ 2!.

It can be written as a sum of positive squares in only one way, i.e., 46656 + 5184 = 216^2 + 72^2 .

It is a tau number, because it is divible by the number of its divisors (80).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 16.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 10366 + ... + 10370.

2^{51840} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 51840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (92565).

51840 is an abundant number, since it is smaller than the sum of its proper divisors (133290).

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

51840 is an equidigital number, since it uses as much as digits as its factorization.

51840 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 31 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 18.

The square root of 51840 is about 227.6839915321. The cubic root of 51840 is about 37.2867900714.

Multiplying 51840 by its product of nonzero digits (160), we get a square (8294400 = 2880^{2}).

51840 divided by its product of nonzero digits (160) gives a square (324 = 18^{2}).

The spelling of 51840 in words is "fifty-one thousand, eight hundred forty".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 32 36 40 45 48 54 60 64 72 80 81 90 96 108 120 128 135 144 160 162 180 192 216 240 270 288 320 324 360 384 405 432 480 540 576 640 648 720 810 864 960 1080 1152 1296 1440 1620 1728 1920 2160 2592 2880 3240 3456 4320 5184 5760 6480 8640 10368 12960 17280 25920 51840

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