39864 has 32 divisors (see below), whose sum is σ = 109440. Its totient is φ = 12000.

The previous prime is 39863. The next prime is 39869. The reversal of 39864 is 46893.

It is a d-powerful number, because it can be written as 3⁵ + 9⁴ + 8⁵ + 6² + 4⁴ .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (39863) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 189 + ... + 339.

It is an arithmetic number, because the mean of its divisors is an integer number (3420).

39864 is a Friedman number, since it can be written as (83+9^4)*6, using all its digits and the basic arithmetic operations.

2³⁹⁸⁶⁴ 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 39864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (54720).

39864 is an abundant number, since it is smaller than the sum of its proper divisors (69576).

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

39864 is a wasteful number, since it uses less digits than its factorization.

39864 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 171 (or 167 counting only the distinct ones).

The product of its digits is 5184, while the sum is 30.

The square root of 39864 is about 199.6597105077. The cubic root of 39864 is about 34.1607154682.

It can be divided in two parts, 39 and 864, that added together give a triangular number (903 = T₄₂).

The spelling of 39864 in words is "thirty-nine thousand, eight hundred sixty-four".