464864400 has 960 divisors, whose sum is σ = 2273187840. Its totient is φ = 87091200.

The previous prime is 464864381. The next prime is 464864419. The reversal of 464864400 is 4468464.

464864400 is a `hidden beast` number, since 4 + 6 + 4 + 8 + 644 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (464864381) and next prime (464864419).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 10810779 + ... + 10810821.

It is an arithmetic number, because the mean of its divisors is an integer number (2367904).

Almost surely, 2^464864400 is an apocalyptic number.

464864400 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 464864400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1136593920).

464864400 is an abundant number, since it is smaller than the sum of its proper divisors (1808323440).

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

464864400 is a wasteful number, since it uses less digits than its factorization.

464864400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 101 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 73728, while the sum is 36.

The square root of 464864400 is about 21560.7142738825. The cubic root of 464864400 is about 774.6557749841.

The spelling of 464864400 in words is "four hundred sixty-four million, eight hundred sixty-four thousand, four hundred".