27682304400 has 405 divisors, whose sum is σ = 99844518241. Its totient is φ = 7102429440.

The previous prime is 27682304389. The next prime is 27682304407. The reversal of 27682304400 is 440328672.

The square root of 27682304400 is 166380.

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

27682304400 is a `hidden beast` number, since 276 + 82 + 304 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 9965629584 + 17716674816 = 99828^2 + 133104^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (27682304407) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 469191571 + ... + 469191629.

Almost surely, 2^27682304400 is an apocalyptic number.

27682304400 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

27682304400 is the 166380-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 27682304400

27682304400 is an abundant number, since it is smaller than the sum of its proper divisors (72162213841).

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

27682304400 is a wasteful number, since it uses less digits than its factorization.

27682304400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 236 (or 116 counting only the distinct ones).

The product of its (nonzero) digits is 64512, while the sum is 36.

Multiplying 27682304400 by its sum of digits (36), we get a square (996562958400 = 998280²).

27682304400 divided by its sum of digits (36) gives a square (768952900 = 27730²).

The spelling of 27682304400 in words is "twenty-seven billion, six hundred eighty-two million, three hundred four thousand, four hundred".