180272 has 20 divisors (see below), whose sum is σ = 368280. Its totient is φ = 85248.

The previous prime is 180263. The next prime is 180281. The reversal of 180272 is 272081.

It is an interprime number because it is at equal distance from previous prime (180263) and next prime (180281).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 180272.

It is an unprimeable number.

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 3 ways as a sum of consecutive naturals, for example, 8 + ... + 600.

It is an arithmetic number, because the mean of its divisors is an integer number (18414).

2¹⁸⁰²⁷² 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 180272, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (184140).

180272 is an abundant number, since it is smaller than the sum of its proper divisors (188008).

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

180272 is a wasteful number, since it uses less digits than its factorization.

180272 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 620 (or 614 counting only the distinct ones).

The product of its (nonzero) digits is 224, while the sum is 20.

The square root of 180272 is about 424.5845027789. The cubic root of 180272 is about 56.4905876194.

Subtracting 180272 from its reverse (272081), we obtain a square (91809 = 303²).

The spelling of 180272 in words is "one hundred eighty thousand, two hundred seventy-two".