852638400 has 588 divisors, whose sum is σ = 3408087672. Its totient is φ = 209018880.

The previous prime is 852638399. The next prime is 852638407. The reversal of 852638400 is 4836258.

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 (852638407) by changing a digit.

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 83 ways as a sum of consecutive naturals, for example, 19828779 + ... + 19828821.

Almost surely, 2^852638400 is an apocalyptic number.

852638400 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 852638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1704043836).

852638400 is an abundant number, since it is smaller than the sum of its proper divisors (2555449272).

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

852638400 is a wasteful number, since it uses less digits than its factorization.

852638400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 100 (or 70 counting only the distinct ones).

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

The square root of 852638400 is about 29199.9726027269. The cubic root of 852638400 is about 948.2473317165.

The spelling of 852638400 in words is "eight hundred fifty-two million, six hundred thirty-eight thousand, four hundred".