13580 has 24 divisors (see below), whose sum is σ = 32928. Its totient is φ = 4608.

The previous prime is 13577. The next prime is 13591. The reversal of 13580 is 8531.

13580 = 41² + 42² + ... + 47².

It is a nialpdrome in base 7.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 92 + ... + 188.

It is an arithmetic number, because the mean of its divisors is an integer number (1372).

2¹³⁵⁸⁰ is an apocalyptic number.

13580 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 13580, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (16464).

13580 is an abundant number, since it is smaller than the sum of its proper divisors (19348).

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

13580 is a wasteful number, since it uses less digits than its factorization.

13580 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 113 (or 111 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 17.

The square root of 13580 is about 116.5332570557. The cubic root of 13580 is about 23.8579572826.

Multiplying 13580 by its sum of digits (17), we get a triangular number (230860 = T₆₇₉).

The spelling of 13580 in words is "thirteen thousand, five hundred eighty".