382800 has 120 divisors (see below), whose sum is σ = 1383840. Its totient is φ = 89600.

The previous prime is 382777. The next prime is 382801. The reversal of 382800 is 8283.

It is a tau number, because it is divible by the number of its divisors (120).

It is a nialpdrome in base 5.

It is a zygodrome in base 5.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 382800.

It is not an unprimeable number, because it can be changed into a prime (382801) by changing a digit.

382800 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 23 ways as a sum of consecutive naturals, for example, 13186 + ... + 13214.

It is an arithmetic number, because the mean of its divisors is an integer number (11532).

2³⁸²⁸⁰⁰ is an apocalyptic number.

382800 is a gapful number since it is divisible by the number (30) 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 382800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (691920).

382800 is an abundant number, since it is smaller than the sum of its proper divisors (1001040).

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

382800 is a wasteful number, since it uses less digits than its factorization.

382800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 61 (or 50 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 21.

The square root of 382800 is about 618.7083319303. The cubic root of 382800 is about 72.6090313500.

The spelling of 382800 in words is "three hundred eighty-two thousand, eight hundred".