468608400 has 720 divisors, whose sum is σ = 2014871040. Its totient is φ = 99532800.

The previous prime is 468608359. The next prime is 468608429. The reversal of 468608400 is 4806864.

468608400 is a `hidden beast` number, since 4 + 6 + 8 + 608 + 40 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (720).

It is a hoax number, since the sum of its digits (36) coincides with the sum of the digits of its distinct prime factors.

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

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 15116385 + ... + 15116415.

It is an arithmetic number, because the mean of its divisors is an integer number (2798432).

Almost surely, 2^468608400 is an apocalyptic number.

468608400 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 468608400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1007435520).

468608400 is an abundant number, since it is smaller than the sum of its proper divisors (1546262640).

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

468608400 is a wasteful number, since it uses less digits than its factorization.

468608400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 104 (or 90 counting only the distinct ones).

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

The square root of 468608400 is about 21647.3647356901. The cubic root of 468608400 is about 776.7298992114.

The spelling of 468608400 in words is "four hundred sixty-eight million, six hundred eight thousand, four hundred".