821648128 has 72 divisors (see below), whose sum is σ = 1918155008. Its totient is φ = 343913472.

The previous prime is 821648117. The next prime is 821648129. The reversal of 821648128 is 821846128.

It is not an unprimeable number, because it can be changed into a prime (821648129) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 71725 + ... + 82387.

Almost surely, 2^821648128 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 821648128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (959077504).

821648128 is an abundant number, since it is smaller than the sum of its proper divisors (1096506880).

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

821648128 is a wasteful number, since it uses less digits than its factorization.

821648128 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 10729 (or 10715 counting only the distinct ones).

The product of its digits is 49152, while the sum is 40.

The square root of 821648128 is about 28664.4052441351. The cubic root of 821648128 is about 936.6168286673.

The spelling of 821648128 in words is "eight hundred twenty-one million, six hundred forty-eight thousand, one hundred twenty-eight".