478288800 has 540 divisors, whose sum is σ = 1948636998. Its totient is φ = 114048000.

The previous prime is 478288787. The next prime is 478288817. The reversal of 478288800 is 8882874.

It can be written as a sum of positive squares in 3 ways, for example, as 214681104 + 263607696 = 14652^2 + 16236^2 .

It is a tau number, because it is divible by the number of its divisors (540).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable 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 89 ways as a sum of consecutive naturals, for example, 7840770 + ... + 7840830.

Almost surely, 2^478288800 is an apocalyptic number.

478288800 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 478288800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (974318499).

478288800 is an abundant number, since it is smaller than the sum of its proper divisors (1470348198).

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

478288800 is a wasteful number, since it uses less digits than its factorization.

478288800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 115 (or 82 counting only the distinct ones).

The product of its (nonzero) digits is 229376, while the sum is 45.

The square root of 478288800 is about 21869.8148140308. The cubic root of 478288800 is about 782.0419868308.

The spelling of 478288800 in words is "four hundred seventy-eight million, two hundred eighty-eight thousand, eight hundred".