828392400 has 480 divisors, whose sum is σ = 3395020800. Its totient is φ = 189734400.

The previous prime is 828392399. The next prime is 828392417. The reversal of 828392400 is 4293828.

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 pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 2257017 + ... + 2257383.

It is an arithmetic number, because the mean of its divisors is an integer number (7072960).

Almost surely, 2^828392400 is an apocalyptic number.

828392400 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 828392400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1697510400).

828392400 is an abundant number, since it is smaller than the sum of its proper divisors (2566628400).

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

828392400 is a wasteful number, since it uses less digits than its factorization.

828392400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 424 (or 407 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

The square root of 828392400 is about 28781.8067535726. The cubic root of 828392400 is about 939.1725024768.

The spelling of 828392400 in words is "eight hundred twenty-eight million, three hundred ninety-two thousand, four hundred".