21121564800 has 384 divisors, whose sum is σ = 82080460800. Its totient is φ = 4671590400.

The previous prime is 21121564787. The next prime is 21121564853. The reversal of 21121564800 is 846512112.

It is a tau number, because it is divible by the number of its divisors (384).

It is a super-3 number, since 3×21121564800³ (a number of 32 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is an unprimeable number.

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 47 ways as a sum of consecutive naturals, for example, 2078131 + ... + 2088269.

It is an arithmetic number, because the mean of its divisors is an integer number (213751200).

Almost surely, 2^21121564800 is an apocalyptic number.

21121564800 is a gapful number since it is divisible by the number (20) 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 21121564800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (41040230400).

21121564800 is an abundant number, since it is smaller than the sum of its proper divisors (60958896000).

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

21121564800 is a wasteful number, since it uses less digits than its factorization.

21121564800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 10204 (or 10187 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 30.

The spelling of 21121564800 in words is "twenty-one billion, one hundred twenty-one million, five hundred sixty-four thousand, eight hundred".