464716800 has 198 divisors, whose sum is σ = 1664730938. Its totient is φ = 123863040.

The previous prime is 464716783. The next prime is 464716807. The reversal of 464716800 is 8617464.

464716800 is a `hidden beast` number, since 4 + 647 + 1 + 6 + 8 + 0 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 84934656 + 379782144 = 9216^2 + 19488^2 .

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

It is not an unprimeable number, because it can be changed into a prime (464716807) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 229392 + ... + 231408.

Almost surely, 2^464716800 is an apocalyptic number.

464716800 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 464716800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (832365469).

464716800 is an abundant number, since it is smaller than the sum of its proper divisors (1200014138).

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

464716800 is a wasteful number, since it uses less digits than its factorization.

464716800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2053 (or 2027 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 36.

The square root of 464716800 is about 21557.2911099702. The cubic root of 464716800 is about 774.5737788179.

The spelling of 464716800 in words is "four hundred sixty-four million, seven hundred sixteen thousand, eight hundred".