39072 has 48 divisors (see below), whose sum is σ = 114912. Its totient is φ = 11520.

The previous prime is 39047. The next prime is 39079. The reversal of 39072 is 27093.

It is a tau number, because it is divible by the number of its divisors (48).

It is not an unprimeable number, because it can be changed into a prime (39079) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1038 + ... + 1074.

It is an arithmetic number, because the mean of its divisors is an integer number (2394).

2³⁹⁰⁷² is an apocalyptic number.

39072 is a gapful number since it is divisible by the number (32) 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 39072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (57456).

39072 is an abundant number, since it is smaller than the sum of its proper divisors (75840).

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

39072 is a wasteful number, since it uses less digits than its factorization.

39072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 61 (or 53 counting only the distinct ones).

The product of its (nonzero) digits is 378, while the sum is 21.

The square root of 39072 is about 197.6663856097. Note that the first 3 decimals coincide. The cubic root of 39072 is about 33.9329705943.

Adding to 39072 its sum of digits (21), we get a palindrome (39093).

The spelling of 39072 in words is "thirty-nine thousand, seventy-two".