478656000 has 320 divisors, whose sum is σ = 1774618560. Its totient is φ = 127180800.

The previous prime is 478655929. The next prime is 478656007. The reversal of 478656000 is 656874.

It is a happy number.

478656000 is a `hidden beast` number, since 47 + 8 + 6 + 5 + 600 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (320).

It is a super-2 number, since 2×478656000² = 458223132672000000, which contains 22 as substring.

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 (478656007) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 1727862 + ... + 1728138.

It is an arithmetic number, because the mean of its divisors is an integer number (5545683).

Almost surely, 2^478656000 is an apocalyptic number.

478656000 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 478656000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (887309280).

478656000 is an abundant number, since it is smaller than the sum of its proper divisors (1295962560).

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

478656000 is an equidigital number, since it uses as much as digits as its factorization.

478656000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 319 (or 287 counting only the distinct ones).

The product of its (nonzero) digits is 40320, while the sum is 36.

The square root of 478656000 is about 21878.2083361504. The cubic root of 478656000 is about 782.2420698209.

The spelling of 478656000 in words is "four hundred seventy-eight million, six hundred fifty-six thousand".