32800 has 36 divisors (see below), whose sum is σ = 82026. Its totient is φ = 12800.

The previous prime is 32797. The next prime is 32801. The reversal of 32800 is 823.

32800 is nontrivially palindromic in base 3, base 9 and base 13.

32800 is an esthetic number in base 15, because in such base its adjacent digits differ by 1.

It can be written as a sum of positive squares in 3 ways, for example, as 15376 + 17424 = 124^2 + 132^2 .

It is a zygodrome in base 3.

It is not an unprimeable number, because it can be changed into a prime (32801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 780 + ... + 820.

2³²⁸⁰⁰ 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 32800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (41013).

32800 is an abundant number, since it is smaller than the sum of its proper divisors (49226).

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

32800 is a wasteful number, since it uses less digits than its factorization.

32800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 61 (or 48 counting only the distinct ones).

The product of its (nonzero) digits is 48, while the sum is 13.

The square root of 32800 is about 181.1077027627. The cubic root of 32800 is about 32.0104132777.

It can be divided in two parts, 32 and 800, that multiplied together give a square (25600 = 160²).

The spelling of 32800 in words is "thirty-two thousand, eight hundred".