21085664400 has 360 divisors, whose sum is σ = 78188689800. Its totient is φ = 5243535360.

The previous prime is 21085664399. The next prime is 21085664429. The reversal of 21085664400 is 446658012.

21085664400 is a `hidden beast` number, since 2 + 1 + 0 + 8 + 5 + 6 + 644 + 0 + 0 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 13719905424 + 7365758976 = 117132^2 + 85824^2 .

It is a tau number, because it is divible by the number of its divisors (360).

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 71 ways as a sum of consecutive naturals, for example, 6914076 + ... + 6917124.

It is an arithmetic number, because the mean of its divisors is an integer number (217190805).

Almost surely, 2^21085664400 is an apocalyptic number.

21085664400 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 21085664400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (39094344900).

21085664400 is an abundant number, since it is smaller than the sum of its proper divisors (57103025400).

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

21085664400 is a wasteful number, since it uses less digits than its factorization.

21085664400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3203 (or 3189 counting only the distinct ones).

The product of its (nonzero) digits is 46080, while the sum is 36.

The spelling of 21085664400 in words is "twenty-one billion, eighty-five million, six hundred sixty-four thousand, four hundred".