13680 has 60 divisors (see below), whose sum is σ = 48360. Its totient is φ = 3456.

The previous prime is 13679. The next prime is 13681. The reversal of 13680 is 8631.

13680 = 3² + 4² + ... + 34².

13680 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (13679) and next prime (13681).

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 congruent number.

It is not an unprimeable number, because it can be changed into a prime (13681) 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 11 ways as a sum of consecutive naturals, for example, 711 + ... + 729.

It is an arithmetic number, because the mean of its divisors is an integer number (806).

2¹³⁶⁸⁰ is an apocalyptic number.

13680 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 13680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (24180).

13680 is an abundant number, since it is smaller than the sum of its proper divisors (34680).

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

13680 is a wasteful number, since it uses less digits than its factorization.

13680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 38 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The square root of 13680 is about 116.9615321377. The cubic root of 13680 is about 23.9163756286.

Adding to 13680 its product of nonzero digits (144), we get a cube (13824 = 24³).

It can be divided in two parts, 136 and 80, that added together give a cube (216 = 6³).

The spelling of 13680 in words is "thirteen thousand, six hundred eighty".