21648384000 has 784 divisors, whose sum is σ = 83802976920. Its totient is φ = 5573836800.

The previous prime is 21648383969. The next prime is 21648384019. The reversal of 21648384000 is 48384612.

21648384000 is a `hidden beast` number, since 2 + 1 + 648 + 3 + 8 + 4 + 0 + 0 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 6596038656 + 15052345344 = 81216^2 + 122688^2 .

It is a super-2 number, since 2×21648384000² (a number of 21 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 55 ways as a sum of consecutive naturals, for example, 746495986 + ... + 746496014.

Almost surely, 2^21648384000 is an apocalyptic number.

21648384000 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 21648384000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (41901488460).

21648384000 is an abundant number, since it is smaller than the sum of its proper divisors (62154592920).

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

21648384000 is an frugal number, since it uses more digits than its factorization.

21648384000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 88 (or 39 counting only the distinct ones).

The product of its (nonzero) digits is 36864, while the sum is 36.

The spelling of 21648384000 in words is "twenty-one billion, six hundred forty-eight million, three hundred eighty-four thousand".