2561738400 has 360 divisors, whose sum is σ = 10064098044. Its totient is φ = 630374400.

The previous prime is 2561738317. The next prime is 2561738407. The reversal of 2561738400 is 48371652.

2561738400 is a `hidden beast` number, since 2 + 5 + 617 + 38 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 1237069584 + 1324668816 = 35172^2 + 36396^2 .

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 not an unprimeable number, because it can be changed into a prime (2561738407) by changing a digit.

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 59 ways as a sum of consecutive naturals, for example, 840880 + ... + 843920.

Almost surely, 2^2561738400 is an apocalyptic number.

2561738400 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 2561738400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5032049022).

2561738400 is an abundant number, since it is smaller than the sum of its proper divisors (7502359644).

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

2561738400 is a wasteful number, since it uses less digits than its factorization.

2561738400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3086 (or 3064 counting only the distinct ones).

The product of its (nonzero) digits is 40320, while the sum is 36.

The square root of 2561738400 is about 50613.6187206566. The cubic root of 2561738400 is about 1368.2903354220.

The spelling of 2561738400 in words is "two billion, five hundred sixty-one million, seven hundred thirty-eight thousand, four hundred".