468800 has 42 divisors (see below), whose sum is σ = 1157478. Its totient is φ = 186880.

The previous prime is 468781. The next prime is 468803. The reversal of 468800 is 8864.

It can be written as a sum of positive squares in 3 ways, for example, as 118336 + 350464 = 344^2 + 592^2 .

It is a self number, because there is not a number n which added to its sum of digits gives 468800.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (468803) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 1454 + ... + 1746.

It is an arithmetic number, because the mean of its divisors is an integer number (27559).

2⁴⁶⁸⁸⁰⁰ is an apocalyptic number.

468800 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 468800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (578739).

468800 is an abundant number, since it is smaller than the sum of its proper divisors (688678).

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

468800 is a wasteful number, since it uses less digits than its factorization.

468800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 315 (or 300 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 26.

The square root of 468800 is about 684.6897107449. The cubic root of 468800 is about 77.6835745351.

The spelling of 468800 in words is "four hundred sixty-eight thousand, eight hundred".