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12768 = 253719
BaseRepresentation
bin11000111100000
3122111220
43013200
5402033
6135040
752140
oct30740
918456
1012768
119658
127480
135a72
144920
153bb3
hex31e0

12768 has 48 divisors (see below), whose sum is σ = 40320. Its totient is φ = 3456.

The previous prime is 12763. The next prime is 12781. The reversal of 12768 is 86721.

It can be divided in two parts, 12 and 768, that multiplied together give a square (9216 = 962).

12768 is nontrivially palindromic in base 15.

It is a Cunningham number, because it is equal to 1132-1.

It is a tau number, because it is divible by the number of its divisors (48).

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 and also a Zuckerman number because it is divisible by the product of its digits.

It is an Ulam number.

It is one of the 548 Lynch-Bell numbers.

It is a zygodrome in base 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (12763) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 663 + ... + 681.

It is an arithmetic number, because the mean of its divisors is an integer number (840).

12768 is a Friedman number, since it can be written as 76*21*8, using all its digits and the basic arithmetic operations.

212768 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 12768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (20160).

12768 is an abundant number, since it is smaller than the sum of its proper divisors (27552).

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

12768 is a wasteful number, since it uses less digits than its factorization.

12768 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 39 (or 31 counting only the distinct ones).

The product of its digits is 672, while the sum is 24.

The square root of 12768 is about 112.9955751346. The cubic root of 12768 is about 23.3726321870.

The spelling of 12768 in words is "twelve thousand, seven hundred sixty-eight".

Divisors: 1 2 3 4 6 7 8 12 14 16 19 21 24 28 32 38 42 48 56 57 76 84 96 112 114 133 152 168 224 228 266 304 336 399 456 532 608 672 798 912 1064 1596 1824 2128 3192 4256 6384 12768