468400800 has 288 divisors, whose sum is σ = 1781136000. Its totient is φ = 106874880.

The previous prime is 468400753. The next prime is 468400831. The reversal of 468400800 is 8004864.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 822916 + ... + 823484.

It is an arithmetic number, because the mean of its divisors is an integer number (6184500).

Almost surely, 2^468400800 is an apocalyptic number.

468400800 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 468400800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (890568000).

468400800 is an abundant number, since it is smaller than the sum of its proper divisors (1312735200).

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

468400800 is a wasteful number, since it uses less digits than its factorization.

468400800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 613 (or 586 counting only the distinct ones).

The product of its (nonzero) digits is 6144, while the sum is 30.

The square root of 468400800 is about 21642.5691635721. The cubic root of 468400800 is about 776.6151815745.

The spelling of 468400800 in words is "four hundred sixty-eight million, four hundred thousand, eight hundred".