827736000 has 448 divisors, whose sum is σ = 3372794880. Its totient is φ = 174182400.

The previous prime is 827735999. The next prime is 827736011. The reversal of 827736000 is 637728.

827736000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (448).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 2183811 + ... + 2184189.

It is an arithmetic number, because the mean of its divisors is an integer number (7528560).

Almost surely, 2^827736000 is an apocalyptic number.

827736000 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 827736000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1686397440).

827736000 is an abundant number, since it is smaller than the sum of its proper divisors (2545058880).

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

827736000 is a wasteful number, since it uses less digits than its factorization.

827736000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 429 (or 409 counting only the distinct ones).

The product of its (nonzero) digits is 14112, while the sum is 33.

The square root of 827736000 is about 28770.4014570530. The cubic root of 827736000 is about 938.9243770197.

The spelling of 827736000 in words is "eight hundred twenty-seven million, seven hundred thirty-six thousand".