827633664 has 312 divisors, whose sum is σ = 2826484752. Its totient is φ = 230031360.

The previous prime is 827633663. The next prime is 827633689. The reversal of 827633664 is 466336728.

827633664 is a `hidden beast` number, since 8 + 2 + 7 + 633 + 6 + 6 + 4 = 666.

It is a tau number, because it is divible by the number of its divisors (312).

It is not an unprimeable number, because it can be changed into a prime (827633663) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 5271474 + ... + 5271630.

It is an arithmetic number, because the mean of its divisors is an integer number (9059246).

Almost surely, 2^827633664 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 827633664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1413242376).

827633664 is an abundant number, since it is smaller than the sum of its proper divisors (1998851088).

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

827633664 is a wasteful number, since it uses less digits than its factorization.

827633664 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 211 (or 186 counting only the distinct ones).

The product of its digits is 870912, while the sum is 45.

The square root of 827633664 is about 28768.6229076054. The cubic root of 827633664 is about 938.8856812177.

It can be divided in two parts, 8 and 27633664, that added together give a palindrome (27633672).

The spelling of 827633664 in words is "eight hundred twenty-seven million, six hundred thirty-three thousand, six hundred sixty-four".