27984 has 40 divisors (see below), whose sum is σ = 80352. Its totient is φ = 8320.

The previous prime is 27983. The next prime is 27997. The reversal of 27984 is 48972.

It is a d-powerful number, because it can be written as **2**^{9} + **7**^{5} + **9**^{4} + **8** + **4**^{6} .

It is a nialpdrome in base 6 and base 8.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (27983) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 502 + ... + 554.

2^{27984} is an apocalyptic number.

27984 is a gapful number since it is divisible by the number (24) 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 27984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (40176).

27984 is an abundant number, since it is smaller than the sum of its proper divisors (52368).

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

27984 is a wasteful number, since it uses less digits than its factorization.

27984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 75 (or 69 counting only the distinct ones).

The product of its digits is 4032, while the sum is 30.

The square root of 27984 is about 167.2841893306. The cubic root of 27984 is about 30.3601046377.

It can be divided in two parts, 279 and 84, that multiplied together give a triangular number (23436 = T_{216}).

The spelling of 27984 in words is "twenty-seven thousand, nine hundred eighty-four".

Divisors: 1 2 3 4 6 8 11 12 16 22 24 33 44 48 53 66 88 106 132 159 176 212 264 318 424 528 583 636 848 1166 1272 1749 2332 2544 3498 4664 6996 9328 13992 27984

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