468532800 has 126 divisors (see below), whose sum is σ = 1665327378. Its totient is φ = 124938240.

The previous prime is 468532769. The next prime is 468532807. The reversal of 468532800 is 8235864.

468532800 is a `hidden beast` number, since 46 + 8 + 532 + 80 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 6110784 + 462422016 = 2472^2 + 21504^2 .

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 (468532807) 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, 1869 + ... + 30668.

Almost surely, 2^468532800 is an apocalyptic number.

468532800 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 468532800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (832663689).

468532800 is an abundant number, since it is smaller than the sum of its proper divisors (1196794578).

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

468532800 is a wasteful number, since it uses less digits than its factorization.

468532800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32565 (or 32547 counting only the distinct ones).

The product of its (nonzero) digits is 46080, while the sum is 36.

The square root of 468532800 is about 21645.6184942819. The cubic root of 468532800 is about 776.6881273478.

The spelling of 468532800 in words is "four hundred sixty-eight million, five hundred thirty-two thousand, eight hundred".