2564407296000 has 2304 divisors, whose sum is σ = 11306458275840. Its totient is φ = 566231040000.

The previous prime is 2564407295953. The next prime is 2564407296041. The reversal of 2564407296000 is 6927044652.

2564407296000 is a `hidden beast` number, since 2 + 56 + 440 + 72 + 96 + 0 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2304).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 82722815985 + ... + 82722816015.

It is an arithmetic number, because the mean of its divisors is an integer number (4907316960).

Almost surely, 2^{2564407296000} is an apocalyptic number.

2564407296000 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 2564407296000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5653229137920).

2564407296000 is an abundant number, since it is smaller than the sum of its proper divisors (8742050979840).

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

2564407296000 is an equidigital number, since it uses as much as digits as its factorization.

2564407296000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 117 (or 69 counting only the distinct ones).

The product of its (nonzero) digits is 725760, while the sum is 45.

The spelling of 2564407296000 in words is "two trillion, five hundred sixty-four billion, four hundred seven million, two hundred ninety-six thousand".