828172800 has 720 divisors, whose sum is σ = 3693930240. Its totient is φ = 172523520.

The previous prime is 828172789. The next prime is 828172801. The reversal of 828172800 is 8271828.

It is a tau number, because it is divible by the number of its divisors (720).

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

It is not an unprimeable number, because it can be changed into a prime (828172801) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 10483161 + ... + 10483239.

Almost surely, 2^828172800 is an apocalyptic number.

828172800 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 828172800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1846965120).

828172800 is an abundant number, since it is smaller than the sum of its proper divisors (2865757440).

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

828172800 is a wasteful number, since it uses less digits than its factorization.

828172800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 133 (or 109 counting only the distinct ones).

The product of its (nonzero) digits is 14336, while the sum is 36.

The square root of 828172800 is about 28777.9915907973. The cubic root of 828172800 is about 939.0895061784.

The spelling of 828172800 in words is "eight hundred twenty-eight million, one hundred seventy-two thousand, eight hundred".