1800 has 36 divisors (see below), whose sum is σ = 6045. Its totient is φ = 480.

The previous prime is 1789. The next prime is 1801. The reversal of 1800 is 81.

Adding to 1800 its reverse (81), we get a palindrome (1881).

1800 = 6^{3} + 7^{3} + ... + 9^{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 can be written as a sum of positive squares in 2 ways, for example, as 1764 + 36 = 42^2 + 6^2 .

It is a tau number, because it is divible by the number of its divisors (36).

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=30.

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.

1800 is an undulating number in base 7.

It is a nialpdrome in base 13 and base 15.

It is not an unprimeable number, because it can be changed into a prime (1801) by changing a digit.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 358 + ... + 362.

2^{1800} is an apocalyptic number.

1800 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 1800

1800 is an abundant number, since it is smaller than the sum of its proper divisors (4245).

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

1800 is a wasteful number, since it uses less digits than its factorization.

1800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 22 (or 10 counting only the distinct ones).

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

The square root of 1800 is about 42.4264068712. The cubic root of 1800 is about 12.1644039911.

The spelling of 1800 in words is "one thousand, eight hundred".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 18 20 24 25 30 36 40 45 50 60 72 75 90 100 120 150 180 200 225 300 360 450 600 900 1800

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