165072 has 40 divisors (see below), whose sum is σ = 451360. Its totient is φ = 51840.

The previous prime is 165059. The next prime is 165079. The reversal of 165072 is 270561.

It is an alternating number because its digits alternate between odd and even.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (165079) by changing a digit.

165072 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 7 ways as a sum of consecutive naturals, for example, 822 + ... + 1002.

It is an arithmetic number, because the mean of its divisors is an integer number (11284).

2¹⁶⁵⁰⁷² is an apocalyptic number.

165072 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 165072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (225680).

165072 is an abundant number, since it is smaller than the sum of its proper divisors (286288).

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

165072 is a wasteful number, since it uses less digits than its factorization.

165072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 211 (or 205 counting only the distinct ones).

The product of its (nonzero) digits is 420, while the sum is 21.

The square root of 165072 is about 406.2905364391. The cubic root of 165072 is about 54.8560422646.

The spelling of 165072 in words is "one hundred sixty-five thousand, seventy-two".