164112 has 40 divisors (see below), whose sum is σ = 458304. Its totient is φ = 50304.

The previous prime is 164093. The next prime is 164113. The reversal of 164112 is 211461.

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is a junction number, because it is equal to n+sod(n) for n = 164091 and 164100.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 164112.

It is not an unprimeable number, because it can be changed into a prime (164113) by changing a digit.

164112 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, 493 + ... + 755.

2¹⁶⁴¹¹² is an apocalyptic number.

164112 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 164112, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (229152).

164112 is an abundant number, since it is smaller than the sum of its proper divisors (294192).

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

164112 is a wasteful number, since it uses less digits than its factorization.

164112 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 287 (or 281 counting only the distinct ones).

The product of its digits is 48, while the sum is 15.

The square root of 164112 is about 405.1073931688. The cubic root of 164112 is about 54.7494943762.

Adding to 164112 its reverse (211461), we get a palindrome (375573).

It can be divided in two parts, 1641 and 12, that added together give a triangular number (1653 = T₅₇).

The spelling of 164112 in words is "one hundred sixty-four thousand, one hundred twelve".