829468800 has 288 divisors, whose sum is σ = 3004026480. Its totient is φ = 217896960.

The previous prime is 829468781. The next prime is 829468819. The reversal of 829468800 is 8864928.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (829468781) and next prime (829468819).

It is a tau number, because it is divible by the number of its divisors (288).

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

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 2390227 + ... + 2390573.

Almost surely, 2^829468800 is an apocalyptic number.

829468800 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

It is a pronic number, being equal to 28800×28801.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 829468800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1502013240).

829468800 is an abundant number, since it is smaller than the sum of its proper divisors (2174557680).

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

829468800 is a wasteful number, since it uses less digits than its factorization.

829468800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 460 (or 440 counting only the distinct ones).

The product of its (nonzero) digits is 221184, while the sum is 45.

The square root of 829468800 is about 28800.4999956598. The cubic root of 829468800 is about 939.5791083870.

The spelling of 829468800 in words is "eight hundred twenty-nine million, four hundred sixty-eight thousand, eight hundred".