12960 has 60 divisors (see below), whose sum is σ = 45738. Its totient is φ = 3456.

The previous prime is 12959. The next prime is 12967. The reversal of 12960 is 6921.

12960 divided by its product of nonzero digits (108) gives a triangular number (120 = T_{15}).

Adding to 12960 its reverse (6921), we get a square (19881 = 141^{2}).

It can be written as a sum of positive squares in only one way, i.e., 11664 + 1296 = 108^2 + 36^2 .

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 12.

It is a Saint-Exupery number, since it is equal to the product of the sides of a Pythagorean triangle: 30 × 18 × 24.

It is not an unprimeable number, because it can be changed into a prime (12967) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 2590 + ... + 2594.

12960 is a Friedman number, since it can be written as 160*9^2, using all its digits and the basic arithmetic operations.

2^{12960} is an apocalyptic number.

12960 is a gapful number since it is divisible by the number (10) 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 12960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (22869).

12960 is an abundant number, since it is smaller than the sum of its proper divisors (32778).

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

12960 is an equidigital number, since it uses as much as digits as its factorization.

12960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 27 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 108, while the sum is 18.

The square root of 12960 is about 113.8419957661. The cubic root of 12960 is about 23.4892058470.

The spelling of 12960 in words is "twelve thousand, nine hundred sixty".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 32 36 40 45 48 54 60 72 80 81 90 96 108 120 135 144 160 162 180 216 240 270 288 324 360 405 432 480 540 648 720 810 864 1080 1296 1440 1620 2160 2592 3240 4320 6480 12960

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