180972 has 36 divisors (see below), whose sum is σ = 500136. Its totient is φ = 54720.

The previous prime is 180959. The next prime is 181001. The reversal of 180972 is 279081.

180972 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

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

180972 is a modest number, since divided by 972 gives 180 as remainder.

It is an unprimeable number.

180972 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 168 + ... + 624.

2¹⁸⁰⁹⁷² is an apocalyptic number.

180972 is a gapful number since it is divisible by the number (12) 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 180972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (250068).

180972 is an abundant number, since it is smaller than the sum of its proper divisors (319164).

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

180972 is a wasteful number, since it uses less digits than its factorization.

180972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 478 (or 473 counting only the distinct ones).

The product of its (nonzero) digits is 1008, while the sum is 27.

The square root of 180972 is about 425.4080394163. The cubic root of 180972 is about 56.5636112334.

It can be divided in two parts, 1809 and 72, that added together give a palindrome (1881).

The spelling of 180972 in words is "one hundred eighty thousand, nine hundred seventy-two".