72084 has 12 divisors (see below), whose sum is σ = 168224. Its totient is φ = 24024.

The previous prime is 72077. The next prime is 72089. The reversal of 72084 is 48027.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (12).

It is a super-2 number, since 2×72084² = 10392206112, which contains 22 as substring.

It is a self number, because there is not a number n which added to its sum of digits gives 72084.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 72084.

It is not an unprimeable number, because it can be changed into a prime (72089) by changing a digit.

72084 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 3 ways as a sum of consecutive naturals, for example, 2992 + ... + 3015.

2⁷²⁰⁸⁴ is an apocalyptic number.

It is an amenable number.

72084 is an abundant number, since it is smaller than the sum of its proper divisors (96140).

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 (84112).

72084 is a wasteful number, since it uses less digits than its factorization.

72084 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 6014 (or 6012 counting only the distinct ones).

The product of its (nonzero) digits is 448, while the sum is 21.

The square root of 72084 is about 268.4846364320. The cubic root of 72084 is about 41.6178486032.

The spelling of 72084 in words is "seventy-two thousand, eighty-four".