468800640 has 576 divisors, whose sum is σ = 2067923520. Its totient is φ = 96768000.

The previous prime is 468800611. The next prime is 468800659. The reversal of 468800640 is 46008864.

468800640 is a `hidden beast` number, since 4 + 6 + 8 + 8 + 0 + 0 + 640 = 666.

It is a tau number, because it is divible by the number of its divisors (576).

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

It is a junction number, because it is equal to n+sod(n) for n = 468800595 and 468800604.

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 71 ways as a sum of consecutive naturals, for example, 3104565 + ... + 3104715.

It is an arithmetic number, because the mean of its divisors is an integer number (3590145).

Almost surely, 2^468800640 is an apocalyptic number.

468800640 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 468800640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1033961760).

468800640 is an abundant number, since it is smaller than the sum of its proper divisors (1599122880).

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

468800640 is a wasteful number, since it uses less digits than its factorization.

468800640 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 201 (or 179 counting only the distinct ones).

The product of its (nonzero) digits is 36864, while the sum is 36.

The square root of 468800640 is about 21651.8045437326. The cubic root of 468800640 is about 776.8360988597.

It can be divided in two parts, 468 and 800640, that added together give a palindrome (801108).

The spelling of 468800640 in words is "four hundred sixty-eight million, eight hundred thousand, six hundred forty".