827632800 has 216 divisors, whose sum is σ = 2961372960. Its totient is φ = 217459200.

The previous prime is 827632787. The next prime is 827632831. The reversal of 827632800 is 8236728.

It is a happy number.

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 35 ways as a sum of consecutive naturals, for example, 510391 + ... + 512009.

It is an arithmetic number, because the mean of its divisors is an integer number (13710060).

Almost surely, 2^827632800 is an apocalyptic number.

827632800 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 827632800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1480686480).

827632800 is an abundant number, since it is smaller than the sum of its proper divisors (2133740160).

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

827632800 is a wasteful number, since it uses less digits than its factorization.

827632800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1716 (or 1700 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 36.

The square root of 827632800 is about 28768.6078912415. The cubic root of 827632800 is about 938.8853545041.

The spelling of 827632800 in words is "eight hundred twenty-seven million, six hundred thirty-two thousand, eight hundred".