165672 has 64 divisors (see below), whose sum is σ = 504000. Its totient is φ = 50112.

The previous prime is 165667. The next prime is 165673. The reversal of 165672 is 276561.

165672 is a `hidden beast` number, since 1 + 656 + 7 + 2 = 666.

It is a super-3 number, since 3×165672³ = 13641703312633344, which contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

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

It is not an unprimeable number, because it can be changed into a prime (165673) by changing a digit.

165672 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 2779 + ... + 2837.

It is an arithmetic number, because the mean of its divisors is an integer number (7875).

2¹⁶⁵⁶⁷² is an apocalyptic number.

165672 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 165672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (252000).

165672 is an abundant number, since it is smaller than the sum of its proper divisors (338328).

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

165672 is a wasteful number, since it uses less digits than its factorization.

165672 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 87 (or 77 counting only the distinct ones).

The product of its digits is 2520, while the sum is 27.

The square root of 165672 is about 407.0282545475. The cubic root of 165672 is about 54.9224250709.

Subtracting 165672 from its reverse (276561), we obtain a square (110889 = 333²).

It can be divided in two parts, 1656 and 72, that added together give a cube (1728 = 12³).

The spelling of 165672 in words is "one hundred sixty-five thousand, six hundred seventy-two".