390400 has 54 divisors (see below), whose sum is σ = 982142. Its totient is φ = 153600.

The previous prime is 390391. The next prime is 390407. The reversal of 390400 is 4093.

390400 is nontrivially palindromic in base 7.

It can be written as a sum of positive squares in 3 ways, for example, as 1024 + 389376 = 32^2 + 624^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is a nialpdrome in base 5.

It is a zygodrome in base 4.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (390407) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 6370 + ... + 6430.

2³⁹⁰⁴⁰⁰ 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 390400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (491071).

390400 is an abundant number, since it is smaller than the sum of its proper divisors (591742).

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

390400 is an equidigital number, since it uses as much as digits as its factorization.

390400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 87 (or 68 counting only the distinct ones).

The product of its (nonzero) digits is 108, while the sum is 16.

The square root of 390400 is about 624.8199740725. The cubic root of 390400 is about 73.0864054745.

Adding to 390400 its reverse (4093), we get a palindrome (394493).

The spelling of 390400 in words is "three hundred ninety thousand, four hundred".