852364800 has 540 divisors, whose sum is σ = 3571898616. Its totient is φ = 193536000.

The previous prime is 852364789. The next prime is 852364801. The reversal of 852364800 is 8463258.

852364800 is a `hidden beast` number, since 8 + 5 + 2 + 3 + 648 + 0 + 0 = 666.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (852364801) by changing a digit.

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 53 ways as a sum of consecutive naturals, for example, 5644725 + ... + 5644875.

Almost surely, 2^852364800 is an apocalyptic number.

852364800 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 852364800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1785949308).

852364800 is an abundant number, since it is smaller than the sum of its proper divisors (2719533816).

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

852364800 is a wasteful number, since it uses less digits than its factorization.

852364800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 199 (or 168 counting only the distinct ones).

The product of its (nonzero) digits is 46080, while the sum is 36.

The square root of 852364800 is about 29195.2872909310. The cubic root of 852364800 is about 948.1458943330.

The spelling of 852364800 in words is "eight hundred fifty-two million, three hundred sixty-four thousand, eight hundred".