13764 has 24 divisors (see below), whose sum is σ = 34048. Its totient is φ = 4320.

The previous prime is 13763. The next prime is 13781. The reversal of 13764 is 46731.

13764 is nontrivially palindromic in base 5.

13764 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a Smith number, since the sum of its digits (21) coincides with the sum of the digits of its prime factors.

It is a self number, because there is not a number n which added to its sum of digits gives 13764.

It is not an unprimeable number, because it can be changed into a prime (13763) 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 7 ways as a sum of consecutive naturals, for example, 354 + ... + 390.

13764 is a Friedman number, since it can be written as 74*31*6, using all its digits and the basic arithmetic operations.

2¹³⁷⁶⁴ is an apocalyptic number.

It is an amenable number.

13764 is an abundant number, since it is smaller than the sum of its proper divisors (20284).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17024).

13764 is a wasteful number, since it uses less digits than its factorization.

13764 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 75 (or 73 counting only the distinct ones).

The product of its digits is 504, while the sum is 21.

The square root of 13764 is about 117.3200750085. The cubic root of 13764 is about 23.9652274216.

It can be divided in two parts, 13 and 764, that added together give a palindrome (777).

The spelling of 13764 in words is "thirteen thousand, seven hundred sixty-four".