2564402400 has 864 divisors, whose sum is σ = 11362897728. Its totient is φ = 530841600.

The previous prime is 2564402381. The next prime is 2564402443. The reversal of 2564402400 is 42044652.

2564402400 is a `hidden beast` number, since 256 + 4 + 4 + 0 + 2 + 400 = 666.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 35128764 + ... + 35128836.

It is an arithmetic number, because the mean of its divisors is an integer number (13151502).

Almost surely, 2^2564402400 is an apocalyptic number.

2564402400 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 2564402400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5681448864).

2564402400 is an abundant number, since it is smaller than the sum of its proper divisors (8798495328).

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

2564402400 is a wasteful number, since it uses less digits than its factorization.

2564402400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 164 (or 148 counting only the distinct ones).

The product of its (nonzero) digits is 7680, while the sum is 27.

The square root of 2564402400 is about 50639.9289099027. The cubic root of 2564402400 is about 1368.7644747328.

It can be divided in two parts, 256440 and 2400, that added together give a triangular number (258840 = T₇₁₉).

The spelling of 2564402400 in words is "two billion, five hundred sixty-four million, four hundred two thousand, four hundred".