19764 has 30 divisors (see below), whose sum is σ = 52514. Its totient is φ = 6480.

The previous prime is 19763. The next prime is 19777. The reversal of 19764 is 46791.

19764 is nontrivially palindromic in base 8.

It can be written as a sum of positive squares in only one way, i.e., 11664 + 8100 = 108^2 + 90^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

19764 is an undulating number in base 8.

It is a nialpdrome in base 12.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (19763) 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 9 ways as a sum of consecutive naturals, for example, 294 + ... + 354.

2¹⁹⁷⁶⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 19764, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (26257).

19764 is an abundant number, since it is smaller than the sum of its proper divisors (32750).

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

19764 is a wasteful number, since it uses less digits than its factorization.

19764 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 77 (or 66 counting only the distinct ones).

The product of its digits is 1512, while the sum is 27.

The square root of 19764 is about 140.5844941663. The cubic root of 19764 is about 27.0369863476.

Adding to 19764 its sum of digits (27), we get a palindrome (19791).

The spelling of 19764 in words is "nineteen thousand, seven hundred sixty-four".