72180 has 36 divisors (see below), whose sum is σ = 219492. Its totient is φ = 19200.

The previous prime is 72173. The next prime is 72211. The reversal of 72180 is 8127.

It can be written as a sum of positive squares in 2 ways, for example, as 54756 + 17424 = 234^2 + 132^2 .

It is a tau number, because it is divible by the number of its divisors (36).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 21 + ... + 380.

It is an arithmetic number, because the mean of its divisors is an integer number (6097).

2⁷²¹⁸⁰ 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 72180, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (109746).

72180 is an abundant number, since it is smaller than the sum of its proper divisors (147312).

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

72180 is a wasteful number, since it uses less digits than its factorization.

72180 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 416 (or 411 counting only the distinct ones).

The product of its (nonzero) digits is 112, while the sum is 18.

The square root of 72180 is about 268.6633581269. The cubic root of 72180 is about 41.6363156748.

It can be divided in two parts, 72 and 180, that added together give a palindrome (252).

The spelling of 72180 in words is "seventy-two thousand, one hundred eighty".