27648000 has 224 divisors, whose sum is σ = 102229920. Its totient is φ = 7372800.

The previous prime is 27647989. The next prime is 27648031. The reversal of 27648000 is 84672.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Jordan-Polya number, since it can be written as (5!)³ ⋅ (2!)⁴.

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 polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 5529598 + ... + 5529602.

Almost surely, 2^27648000 is an apocalyptic number.

27648000 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 27648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (51114960).

27648000 is an abundant number, since it is smaller than the sum of its proper divisors (74581920).

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

27648000 is an frugal number, since it uses more digits than its factorization.

27648000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 50 (or 10 counting only the distinct ones).

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

The square root of 27648000 is about 5258.1365520496. The cubic root of 27648000 is about 302.3810519748.

The spelling of 27648000 in words is "twenty-seven million, six hundred forty-eight thousand".