28800 has 72 divisors (see below), whose sum is σ = 102765. Its totient is φ = 7680.

The previous prime is 28793. The next prime is 28807. The reversal of 28800 is 882.

28800 = 7^{3} + 8^{3} + ... + 18^{3}.

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.

It is a Jordan-Polya number, since it can be written as (5!)^{2} ⋅ 2!.

It is an interprime number because it is at equal distance from previous prime (28793) and next prime (28807).

It can be written as a sum of positive squares in 2 ways, for example, as 28224 + 576 = 168^2 + 24^2 .

It is a tau number, because it is divible by the number of its divisors (72).

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=120.

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

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a nialpdrome in base 15.

It is a zygodrome in base 15.

It is not an unprimeable number, because it can be changed into a prime (28807) by changing a digit.

28800 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 8 ways as a sum of consecutive naturals, for example, 5758 + ... + 5762.

2^{28800} is an apocalyptic number.

28800 is a gapful number since it is divisible by the number (20) 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 28800

28800 is an abundant number, since it is smaller than the sum of its proper divisors (73965).

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

28800 is a wasteful number, since it uses less digits than its factorization.

28800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 30 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 18.

The square root of 28800 is about 169.7056274848. The cubic root of 28800 is about 30.6523772957.

Subtracting from 28800 its sum of digits (18), we obtain a palindrome (28782).

Multiplying 28800 by its sum of digits (18), we get a square (518400 = 720^{2}).

28800 divided by its sum of digits (18) gives a square (1600 = 40^{2}).

Multiplying 28800 by its product of nonzero digits (128), we get a square (3686400 = 1920^{2}).

28800 divided by its product of nonzero digits (128) gives a square (225 = 15^{2}).

Multiplying 28800 by its reverse (882), we get a square (25401600 = 5040^{2}).

It can be divided in two parts, 28 and 800, that added together give a palindrome (828).

The spelling of 28800 in words is "twenty-eight thousand, eight hundred".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 32 36 40 45 48 50 60 64 72 75 80 90 96 100 120 128 144 150 160 180 192 200 225 240 288 300 320 360 384 400 450 480 576 600 640 720 800 900 960 1152 1200 1440 1600 1800 1920 2400 2880 3200 3600 4800 5760 7200 9600 14400 28800

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