825120800 has 288 divisors, whose sum is σ = 2449843200. Its totient is φ = 270950400.

The previous prime is 825120799. The next prime is 825120853. The reversal of 825120800 is 8021528.

It is a harmonic number, since the harmonic mean of its divisors is an integer.

It is a self number, because there is not a number n which added to its sum of digits gives 825120800.

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 47 ways as a sum of consecutive naturals, for example, 8506352 + ... + 8506448.

It is an arithmetic number, because the mean of its divisors is an integer number (8506400).

Almost surely, 2^825120800 is an apocalyptic number.

825120800 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 825120800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1224921600).

825120800 is an abundant number, since it is smaller than the sum of its proper divisors (1624722400).

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

825120800 is a wasteful number, since it uses less digits than its factorization.

825120800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 169 (or 142 counting only the distinct ones).

The product of its (nonzero) digits is 1280, while the sum is 26.

The square root of 825120800 is about 28724.9160138024. The cubic root of 825120800 is about 937.9345019982.

The spelling of 825120800 in words is "eight hundred twenty-five million, one hundred twenty thousand, eight hundred".