21312958464000 has 4608 divisors, whose sum is σ = 101815847078400. Its totient is φ = 4414478745600.

The previous prime is 21312958463999. The next prime is 21312958464001. The reversal of 21312958464000 is 46485921312.

21312958464000 is a `hidden beast` number, since 2 + 1 + 3 + 1 + 2 + 9 + 584 + 64 + 0 + 0 + 0 = 666.

21312958464000 is digitally balanced in base 5, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (21312958463999) and next prime (21312958464001).

It is a tau number, because it is divible by the number of its divisors (4608).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (21312958464001) by changing a digit.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 926650367989 + ... + 926650368011.

It is an arithmetic number, because the mean of its divisors is an integer number (22095452925).

Almost surely, 2^{21312958464000} is an apocalyptic number.

21312958464000 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 21312958464000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (50907923539200).

21312958464000 is an abundant number, since it is smaller than the sum of its proper divisors (80502888614400).

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

21312958464000 is an frugal number, since it uses more digits than its factorization.

21312958464000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 116 (or 59 counting only the distinct ones).

The product of its (nonzero) digits is 414720, while the sum is 45.

The spelling of 21312958464000 in words is "twenty-one trillion, three hundred twelve billion, nine hundred fifty-eight million, four hundred sixty-four thousand".