165312 has 84 divisors (see below), whose sum is σ = 554736. Its totient is φ = 46080.

The previous prime is 165311. The next prime is 165313. The reversal of 165312 is 213561.

165312 is a `hidden beast` number, since 1 + 653 + 12 = 666.

It is an interprime number because it is at equal distance from previous prime (165311) and next prime (165313).

It is a tau number, because it is divible by the number of its divisors (84).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (165311) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4012 + ... + 4052.

It is an arithmetic number, because the mean of its divisors is an integer number (6604).

2¹⁶⁵³¹² is an apocalyptic number.

165312 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 165312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (277368).

165312 is an abundant number, since it is smaller than the sum of its proper divisors (389424).

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

165312 is a wasteful number, since it uses less digits than its factorization.

165312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 66 (or 53 counting only the distinct ones).

The product of its digits is 180, while the sum is 18.

The square root of 165312 is about 406.5857843063. The cubic root of 165312 is about 54.8826146590.

Adding to 165312 its reverse (213561), we get a palindrome (378873).

The spelling of 165312 in words is "one hundred sixty-five thousand, three hundred twelve".