478612800 has 252 divisors, whose sum is σ = 1765539776. Its totient is φ = 127526400.

The previous prime is 478612789. The next prime is 478612807. The reversal of 478612800 is 8216874.

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 (478612807) by changing a digit.

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 35 ways as a sum of consecutive naturals, for example, 388185 + ... + 389415.

Almost surely, 2^478612800 is an apocalyptic number.

478612800 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 478612800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (882769888).

478612800 is an abundant number, since it is smaller than the sum of its proper divisors (1286926976).

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

478612800 is a wasteful number, since it uses less digits than its factorization.

478612800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1268 (or 1241 counting only the distinct ones).

The product of its (nonzero) digits is 21504, while the sum is 36.

The square root of 478612800 is about 21877.2210301034. The cubic root of 478612800 is about 782.2185359579.

It can be divided in two parts, 478 and 612800, that added together give a triangular number (613278 = T₁₁₀₇).

The spelling of 478612800 in words is "four hundred seventy-eight million, six hundred twelve thousand, eight hundred".