478108800 has 288 divisors, whose sum is σ = 1838671380. Its totient is φ = 117596160.

The previous prime is 478108793. The next prime is 478108871. The reversal of 478108800 is 8801874.

478108800 is a `hidden beast` number, since 478 + 108 + 80 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 121352256 + 356756544 = 11016^2 + 18888^2 .

It is a tau number, because it is divible by the number of its divisors (288).

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

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 373762 + ... + 375038.

Almost surely, 2^478108800 is an apocalyptic number.

478108800 is a gapful number since it is divisible by the number (40) 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 478108800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (919335690).

478108800 is an abundant number, since it is smaller than the sum of its proper divisors (1360562580).

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

478108800 is a wasteful number, since it uses less digits than its factorization.

478108800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1320 (or 1300 counting only the distinct ones).

The product of its (nonzero) digits is 14336, while the sum is 36.

The square root of 478108800 is about 21865.6991655881. The cubic root of 478108800 is about 781.9438695286.

It can be divided in two parts, 478 and 108800, that added together give a triangular number (109278 = T₄₆₇).

The spelling of 478108800 in words is "four hundred seventy-eight million, one hundred eight thousand, eight hundred".