464032800 has 864 divisors, whose sum is σ = 2183860224. Its totient is φ = 93312000.

The previous prime is 464032787. The next prime is 464032847. The reversal of 464032800 is 8230464.

It is a tau number, because it is divible by the number of its divisors (864).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

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 143 ways as a sum of consecutive naturals, for example, 14968785 + ... + 14968815.

It is an arithmetic number, because the mean of its divisors is an integer number (2527616).

Almost surely, 2^464032800 is an apocalyptic number.

464032800 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 464032800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1091930112).

464032800 is an abundant number, since it is smaller than the sum of its proper divisors (1719827424).

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

464032800 is a wasteful number, since it uses less digits than its factorization.

464032800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 84 (or 59 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 27.

The square root of 464032800 is about 21541.4205659701. The cubic root of 464032800 is about 774.1935697581.

The spelling of 464032800 in words is "four hundred sixty-four million, thirty-two thousand, eight hundred".