2506585568400 has 135 divisors (see below), whose sum is σ = 8698877861401. Its totient is φ = 668397486720.

The previous prime is 2506585568371. The next prime is 2506585568413. The reversal of 2506585568400 is 48655856052.

It is a happy number.

The square root of 2506585568400 is 1583220.

It is a perfect power (a square), and thus also a powerful number.

2506585568400 is a `hidden beast` number, since 2 + 5 + 0 + 6 + 5 + 8 + 556 + 84 + 0 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 902370804624 + 1604214763776 = 949932^2 + 1266576^2 .

It is a super-2 number, since 2×2506585568400² (a number of 26 digits) contains 22 as substring.

It is a Duffinian number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 94980007 + ... + 95006393.

Almost surely, 2^{2506585568400} is an apocalyptic number.

2506585568400 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

2506585568400 is the 1583220-th square number.

It is an amenable number.

2506585568400 is an abundant number, since it is smaller than the sum of its proper divisors (6192292293001).

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

2506585568400 is an frugal number, since it uses more digits than its factorization.

2506585568400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 52798 (or 26397 counting only the distinct ones).

The product of its (nonzero) digits is 11520000, while the sum is 54.

The spelling of 2506585568400 in words is "two trillion, five hundred six billion, five hundred eighty-five million, five hundred sixty-eight thousand, four hundred".