825386400 has 432 divisors, whose sum is σ = 3107613600. Its totient is φ = 205793280.

The previous prime is 825386357. The next prime is 825386447. The reversal of 825386400 is 4683528.

825386400 is a `hidden beast` number, since 8 + 2 + 5 + 3 + 8 + 640 + 0 = 666.

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

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 12319167 + ... + 12319233.

It is an arithmetic number, because the mean of its divisors is an integer number (7193550).

Almost surely, 2^825386400 is an apocalyptic number.

825386400 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 825386400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1553806800).

825386400 is an abundant number, since it is smaller than the sum of its proper divisors (2282227200).

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

825386400 is a wasteful number, since it uses less digits than its factorization.

825386400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 181 (or 165 counting only the distinct ones).

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

The square root of 825386400 is about 28729.5388059050. The cubic root of 825386400 is about 938.0351291545.

The spelling of 825386400 in words is "eight hundred twenty-five million, three hundred eighty-six thousand, four hundred".