13500 has 48 divisors (see below), whose sum is σ = 43680. Its totient is φ = 3600.

The previous prime is 13499. The next prime is 13513. The reversal of 13500 is 531.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

13500 is nontrivially palindromic in base 14.

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a plaindrome in base 16.

It is a nialpdrome in base 15.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 2698 + ... + 2702.

It is an arithmetic number, because the mean of its divisors is an integer number (910).

2¹³⁵⁰⁰ is an apocalyptic number.

13500 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 13500, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (21840).

13500 is an abundant number, since it is smaller than the sum of its proper divisors (30180).

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

13500 is a wasteful number, since it uses less digits than its factorization.

13500 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 28 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 15, while the sum is 9.

The square root of 13500 is about 116.1895003862. The cubic root of 13500 is about 23.8110157795.

Multiplying 13500 by its product of nonzero digits (15), we get a square (202500 = 450²).

13500 divided by its product of nonzero digits (15) gives a square (900 = 30²).

The spelling of 13500 in words is "thirteen thousand, five hundred".