828032400 has 270 divisors, whose sum is σ = 3113830278. Its totient is φ = 203673600.

The previous prime is 828032399. The next prime is 828032437. The reversal of 828032400 is 4230828.

It can be written as a sum of positive squares in 9 ways, for example, as 661312656 + 166719744 = 25716^2 + 12912^2 .

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, 607720 + ... + 609080.

Almost surely, 2^828032400 is an apocalyptic number.

828032400 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 828032400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1556915139).

828032400 is an abundant number, since it is smaller than the sum of its proper divisors (2285797878).

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

828032400 is a wasteful number, since it uses less digits than its factorization.

828032400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1411 (or 1384 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

The square root of 828032400 is about 28775.5521232869. The cubic root of 828032400 is about 939.0364352822.

The spelling of 828032400 in words is "eight hundred twenty-eight million, thirty-two thousand, four hundred".