2688 has 32 divisors (see below), whose sum is σ = 8160. Its totient is φ = 768.

The previous prime is 2687. The next prime is 2689. The reversal of 2688 is 8862.

It is an interprime number because it is at equal distance from previous prime (2687) and next prime (2689).

It is a tau number, because it is divible by the number of its divisors (32).

It is a Smith number, since the sum of its digits (24) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a nude number because it is divisible by every one of its digits.

Its product of digits (768) is a multiple of the sum of its prime divisors (12).

It is a plaindrome in base 10.

It is a nialpdrome in base 4, base 8, base 14 and base 16.

It is a zygodrome in base 4.

It is not an unprimeable number, because it can be changed into a prime (2683) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 381 + ... + 387.

It is an arithmetic number, because the mean of its divisors is an integer number (255).

2688 is a gapful number since it is divisible by the number (28) 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 2688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4080).

2688 is an abundant number, since it is smaller than the sum of its proper divisors (5472).

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

2688 is an equidigital number, since it uses as much as digits as its factorization.

2688 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 24 (or 12 counting only the distinct ones).

The product of its digits is 768, while the sum is 24.

The square root of 2688 is about 51.8459255873. The cubic root of 2688 is about 13.9041065795.

It can be divided in two parts, 268 and 8, that added together give a triangular number (276 = T_{23}).

The spelling of 2688 in words is "two thousand, six hundred eighty-eight".

Divisors: 1 2 3 4 6 7 8 12 14 16 21 24 28 32 42 48 56 64 84 96 112 128 168 192 224 336 384 448 672 896 1344 2688

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