27006314400 has 216 divisors, whose sum is σ = 102556834380. Its totient is φ = 6647685120.

The previous prime is 27006314383. The next prime is 27006314431. The reversal of 27006314400 is 441360072.

27006314400 is a `hidden beast` number, since 27 + 0 + 0 + 631 + 4 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 12586147344 + 14420167056 = 112188^2 + 120084^2 .

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 35 ways as a sum of consecutive naturals, for example, 50665 + ... + 237864.

Almost surely, 2^27006314400 is an apocalyptic number.

27006314400 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 27006314400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (51278417190).

27006314400 is an abundant number, since it is smaller than the sum of its proper divisors (75550519980).

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

27006314400 is a wasteful number, since it uses less digits than its factorization.

27006314400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 288568 (or 288552 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 27.

Adding to 27006314400 its reverse (441360072), we get a palindrome (27447674472).

The spelling of 27006314400 in words is "twenty-seven billion, six million, three hundred fourteen thousand, four hundred".