10800 has 60 divisors (see below), whose sum is σ = 38440. Its totient is φ = 2880.

The previous prime is 10799. The next prime is 10831. The reversal of 10800 is 801.

Subtracting from 10800 its reverse (801), we obtain a palindrome (9999).

It can be divided in two parts, 10 and 800, that multiplied together give a cube (8000 = 20^{3}).

10800 = T_{16} + T_{17} + ... +
T_{40}.

10800 = 6^{3} + 7^{3} + ... + 14^{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 tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (9).

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 12 and base 15.

It is a zygodrome in base 3 and base 15.

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 11 ways as a sum of consecutive naturals, for example, 2158 + ... + 2162.

2^{10800} is an apocalyptic number.

10800 is a gapful number since it is divisible by the number (10) 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 10800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (19220).

10800 is an abundant number, since it is smaller than the sum of its proper divisors (27640).

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

10800 is a wasteful number, since it uses less digits than its factorization.

10800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 27 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 8, while the sum is 9.

The square root of 10800 is about 103.9230484541. The cubic root of 10800 is about 22.1041889918.

The spelling of 10800 in words is "ten thousand, eight hundred".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 36 40 45 48 50 54 60 72 75 80 90 100 108 120 135 144 150 180 200 216 225 240 270 300 360 400 432 450 540 600 675 720 900 1080 1200 1350 1800 2160 2700 3600 5400 10800

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