829310400 has 378 divisors, whose sum is σ = 3099521360. Its totient is φ = 218350080.

The previous prime is 829310399. The next prime is 829310413. The reversal of 829310400 is 4013928.

It is a Harshad number since it is a multiple of its sum of digits (27).

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 53 ways as a sum of consecutive naturals, for example, 10497561 + ... + 10497639.

Almost surely, 2^829310400 is an apocalyptic number.

829310400 is a gapful number since it is divisible by the number (80) 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 829310400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1549760680).

829310400 is an abundant number, since it is smaller than the sum of its proper divisors (2270210960).

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

829310400 is an frugal number, since it uses more digits than its factorization.

829310400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 125 (or 89 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 829310400 is about 28797.7499121025. The cubic root of 829310400 is about 939.5192954860.

The spelling of 829310400 in words is "eight hundred twenty-nine million, three hundred ten thousand, four hundred".