27864000 has 280 divisors, whose sum is σ = 105479088. Its totient is φ = 7257600.

The previous prime is 27863993. The next prime is 27864047. The reversal of 27864000 is 46872.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

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 39 ways as a sum of consecutive naturals, for example, 647979 + ... + 648021.

Almost surely, 2^27864000 is an apocalyptic number.

27864000 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 27864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (52739544).

27864000 is an abundant number, since it is smaller than the sum of its proper divisors (77615088).

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

27864000 is an equidigital number, since it uses as much as digits as its factorization.

27864000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 82 (or 53 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The square root of 27864000 is about 5278.6361875015. The cubic root of 27864000 is about 303.1664608325.

It can be divided in two parts, 2786 and 4000, that added together give a triangular number (6786 = T₁₁₆).

The spelling of 27864000 in words is "twenty-seven million, eight hundred sixty-four thousand".