829872000 has 512 divisors, whose sum is σ = 3265142400. Its totient is φ = 206438400.

The previous prime is 829871969. The next prime is 829872023. The reversal of 829872000 is 278928.

829872000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 7343944 + ... + 7344056.

Almost surely, 2^829872000 is an apocalyptic number.

829872000 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 829872000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1632571200).

829872000 is an abundant number, since it is smaller than the sum of its proper divisors (2435270400).

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

829872000 is a wasteful number, since it uses less digits than its factorization.

829872000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 168 (or 140 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 36.

The square root of 829872000 is about 28807.4990236917. The cubic root of 829872000 is about 939.7313250544.

The spelling of 829872000 in words is "eight hundred twenty-nine million, eight hundred seventy-two thousand".