827668800 has 1008 divisors, whose sum is σ = 3877787520. Its totient is φ = 170311680.

The previous prime is 827668789. The next prime is 827668813. The reversal of 827668800 is 8866728.

It is a tau number, because it is divible by the number of its divisors (1008).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 35985589 + ... + 35985611.

Almost surely, 2^827668800 is an apocalyptic number.

827668800 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 827668800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1938893760).

827668800 is an abundant number, since it is smaller than the sum of its proper divisors (3050118720).

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

827668800 is a wasteful number, since it uses less digits than its factorization.

827668800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 85 (or 57 counting only the distinct ones).

The product of its (nonzero) digits is 258048, while the sum is 45.

The square root of 827668800 is about 28769.2335664334. The cubic root of 827668800 is about 938.8989673779.

The spelling of 827668800 in words is "eight hundred twenty-seven million, six hundred sixty-eight thousand, eight hundred".