827964181340352 has 672 divisors, whose sum is σ = 2938686064704000. Its totient is φ = 217567584976896.

The previous prime is 827964181340347. The next prime is 827964181340383. The reversal of 827964181340352 is 253043181469728.

It is a happy number.

827964181340352 is a `hidden beast` number, since 8 + 2 + 7 + 9 + 64 + 181 + 3 + 40 + 352 = 666.

It is a tau number, because it is divible by the number of its divisors (672).

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a self number, because there is not a number n which added to its sum of digits gives 827964181340352.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 1272363423 + ... + 1273013985.

It is a 2-persistent number, because it is pandigital, and so is 2⋅827964181340352 = 1655928362680704, but 3⋅827964181340352 = 2483892544021056 is not.

Almost surely, 2^{827964181340352} 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 827964181340352, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1469343032352000).

827964181340352 is an abundant number, since it is smaller than the sum of its proper divisors (2110721883363648).

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

827964181340352 is a wasteful number, since it uses less digits than its factorization.

827964181340352 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 651093 (or 651080 counting only the distinct ones).

The product of its (nonzero) digits is 69672960, while the sum is 63.

The spelling of 827964181340352 in words is "eight hundred twenty-seven trillion, nine hundred sixty-four billion, one hundred eighty-one million, three hundred forty thousand, three hundred fifty-two".