386400 has 144 divisors (see below), whose sum is σ = 1499904. Its totient is φ = 84480.

The previous prime is 386383. The next prime is 386401. The reversal of 386400 is 4683.

It is a Harshad number since it is a multiple of its sum of digits (21).

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 386400.

It is not an unprimeable number, because it can be changed into a prime (386401) by changing a digit.

386400 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, 16789 + ... + 16811.

It is an arithmetic number, because the mean of its divisors is an integer number (10416).

386400 is a Friedman number, since it can be written as 300*(6^4-8), using all its digits and the basic arithmetic operations.

2³⁸⁶⁴⁰⁰ is an apocalyptic number.

386400 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 386400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (749952).

386400 is an abundant number, since it is smaller than the sum of its proper divisors (1113504).

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

386400 is a wasteful number, since it uses less digits than its factorization.

386400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 53 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 21.

The square root of 386400 is about 621.6108107168. The cubic root of 386400 is about 72.8359360479.

The spelling of 386400 in words is "three hundred eighty-six thousand, four hundred".