478968000 has 224 divisors, whose sum is σ = 1808122368. Its totient is φ = 109440000.

The previous prime is 478967971. The next prime is 478968001. The reversal of 478968000 is 869874.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (224).

It is a Harshad number since it is a multiple of its sum of digits (42).

It is not an unprimeable number, because it can be changed into a prime (478968001) 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, 166575 + ... + 169425.

Almost surely, 2^478968000 is an apocalyptic number.

478968000 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 478968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (904061184).

478968000 is an abundant number, since it is smaller than the sum of its proper divisors (1329154368).

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

478968000 is a wasteful number, since it uses less digits than its factorization.

478968000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2888 (or 2868 counting only the distinct ones).

The product of its (nonzero) digits is 96768, while the sum is 42.

The square root of 478968000 is about 21885.3375573693. The cubic root of 478968000 is about 782.4119945803.

The spelling of 478968000 in words is "four hundred seventy-eight million, nine hundred sixty-eight thousand".