468295214400 has 756 divisors, whose sum is σ = 1869328292832. Its totient is φ = 115256494080.

The previous prime is 468295214369. The next prime is 468295214417. The reversal of 468295214400 is 4412592864.

It is a happy number.

468295214400 is a `hidden beast` number, since 4 + 6 + 8 + 29 + 5 + 214 + 400 = 666.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 65703637 + ... + 65710763.

It is an arithmetic number, because the mean of its divisors is an integer number (2472656472).

Almost surely, 2^468295214400 is an apocalyptic number.

468295214400 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 468295214400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (934664146416).

468295214400 is an abundant number, since it is smaller than the sum of its proper divisors (1401033078432).

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

468295214400 is a wasteful number, since it uses less digits than its factorization.

468295214400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 7190 (or 7150 counting only the distinct ones).

The product of its (nonzero) digits is 552960, while the sum is 45.

The spelling of 468295214400 in words is "four hundred sixty-eight billion, two hundred ninety-five million, two hundred fourteen thousand, four hundred".