380400 has 60 divisors (see below), whose sum is σ = 1222392. Its totient is φ = 101120.

The previous prime is 380383. The next prime is 380417. The reversal of 380400 is 4083.

It is an interprime number because it is at equal distance from previous prime (380383) and next prime (380417).

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 380400.

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 380400.

It is an unprimeable number.

380400 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 (11) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1042 + ... + 1358.

2³⁸⁰⁴⁰⁰ is an apocalyptic number.

380400 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 380400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (611196).

380400 is an abundant number, since it is smaller than the sum of its proper divisors (841992).

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

380400 is a wasteful number, since it uses less digits than its factorization.

380400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 338 (or 327 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 15.

The square root of 380400 is about 616.7657578044. The cubic root of 380400 is about 72.4569701062.

Adding to 380400 its reverse (4083), we get a palindrome (384483).

It can be divided in two parts, 380 and 400, that added together give a triangular number (780 = T₃₉).

The spelling of 380400 in words is "three hundred eighty thousand, four hundred".