398400 has 84 divisors (see below), whose sum is σ = 1322832. Its totient is φ = 104960.

The previous prime is 398393. The next prime is 398407. The reversal of 398400 is 4893.

398400 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (398393) and next prime (398407).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is not an unprimeable number, because it can be changed into a prime (398407) by changing a digit.

398400 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4759 + ... + 4841.

It is an arithmetic number, because the mean of its divisors is an integer number (15748).

2³⁹⁸⁴⁰⁰ is an apocalyptic number.

398400 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 398400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (661416).

398400 is an abundant number, since it is smaller than the sum of its proper divisors (924432).

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

398400 is a wasteful number, since it uses less digits than its factorization.

398400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 108 (or 93 counting only the distinct ones).

The product of its (nonzero) digits is 864, while the sum is 24.

The square root of 398400 is about 631.1893535224. The cubic root of 398400 is about 73.5822578532.

The spelling of 398400 in words is "three hundred ninety-eight thousand, four hundred".