27648 has 44 divisors (see below), whose sum is σ = 81880. Its totient is φ = 9216.

The previous prime is 27647. The next prime is 27653. The reversal of 27648 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 (4!)^{3} ⋅ 2!.

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

It is a nialpdrome in base 6 and base 8.

It is a zygodrome in base 8.

It is not an unprimeable number, because it can be changed into a prime (27647) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 9215 + 9216 + 9217.

27648 is a Friedman number, since it can be written as 4^6*(7-2/8), using all its digits and the basic arithmetic operations.

2^{27648} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 27648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (40940).

27648 is an abundant number, since it is smaller than the sum of its proper divisors (54232).

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

27648 is an equidigital number, since it uses as much as digits as its factorization.

27648 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 29 (or 5 counting only the distinct ones).

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

The square root of 27648 is about 166.2768775266. The cubic root of 27648 is about 30.2381051975.

Multiplying 27648 by its sum of digits (27), we get a square (746496 = 864^{2}).

27648 divided by its sum of digits (27) gives a 10-th power (1024 = 2^{10}).

Multiplying 27648 by its reverse (84672), we get a square (2341011456 = 48384^{2}).

It can be divided in two parts, 2764 and 8, that added together give a palindrome (2772).

The spelling of 27648 in words is "twenty-seven thousand, six hundred forty-eight".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 96 108 128 144 192 216 256 288 384 432 512 576 768 864 1024 1152 1536 1728 2304 3072 3456 4608 6912 9216 13824 27648

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