363398400 has 270 divisors, whose sum is σ = 1345566222. Its totient is φ = 96768000.

The previous prime is 363398381. The next prime is 363398401. The reversal of 363398400 is 4893363.

It can be written as a sum of positive squares in 3 ways, for example, as 69755904 + 293642496 = 8352^2 + 17136^2 .

It is a tau number, because it is divible by the number of its divisors (270).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (363398401) by changing a digit.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 518050 + ... + 518750.

Almost surely, 2^363398400 is an apocalyptic number.

363398400 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 363398400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (672783111).

363398400 is an abundant number, since it is smaller than the sum of its proper divisors (982167822).

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

363398400 is an equidigital number, since it uses as much as digits as its factorization.

363398400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 739 (or 711 counting only the distinct ones).

The product of its (nonzero) digits is 46656, while the sum is 36.

The square root of 363398400 is about 19063.0113046182. The cubic root of 363398400 is about 713.6101254035.

The spelling of 363398400 in words is "three hundred sixty-three million, three hundred ninety-eight thousand, four hundred".