64800 has 90 divisors (see below), whose sum is σ = 236313. Its totient is φ = 17280.

The previous prime is 64793. The next prime is 64811. The reversal of 64800 is 846.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

64800 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 2 ways, for example, as 63504 + 1296 = 252^2 + 36^2 .

It is a tau number, because it is divible by the number of its divisors (90).

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=180.

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.

64800 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 14 ways as a sum of consecutive naturals, for example, 12958 + ... + 12962.

2^{64800} is an apocalyptic number.

64800 is a gapful number since it is divisible by the number (60) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 64800

64800 is an abundant number, since it is smaller than the sum of its proper divisors (171513).

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

64800 is a wasteful number, since it uses less digits than its factorization.

64800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 64800 is about 254.5584412272. The cubic root of 64800 is about 40.1659770049.

Multiplying 64800 by its sum of digits (18), we get a square (1166400 = 1080^{2}).

64800 divided by its sum of digits (18) gives a square (3600 = 60^{2}).

The spelling of 64800 in words is "sixty-four thousand, eight hundred".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54 60 72 75 80 81 90 96 100 108 120 135 144 150 160 162 180 200 216 225 240 270 288 300 324 360 400 405 432 450 480 540 600 648 675 720 800 810 864 900 1080 1200 1296 1350 1440 1620 1800 2025 2160 2400 2592 2700 3240 3600 4050 4320 5400 6480 7200 8100 10800 12960 16200 21600 32400 64800

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