27728000 has 64 divisors (see below), whose sum is σ = 68978520. Its totient is φ = 11084800.

The previous prime is 27727963. The next prime is 27728027. The reversal of 27728000 is 82772.

It can be written as a sum of positive squares in 4 ways, for example, as 7441984 + 20286016 = 2728^2 + 4504^2 .

It is a tau number, because it is divible by the number of its divisors (64).

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 15134 + ... + 16866.

Almost surely, 2^27728000 is an apocalyptic number.

27728000 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 27728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (34489260).

27728000 is an abundant number, since it is smaller than the sum of its proper divisors (41250520).

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

27728000 is an equidigital number, since it uses as much as digits as its factorization.

27728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1762 (or 1740 counting only the distinct ones).

The product of its (nonzero) digits is 1568, while the sum is 26.

The square root of 27728000 is about 5265.7383148045. The cubic root of 27728000 is about 302.6724195206.

The spelling of 27728000 in words is "twenty-seven million, seven hundred twenty-eight thousand".