168072 has 32 divisors (see below), whose sum is σ = 432000. Its totient is φ = 54464.

The previous prime is 168071. The next prime is 168083. The reversal of 168072 is 270861.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 168072.

It is not an unprimeable number, because it can be changed into a prime (168071) by changing a digit.

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 7 ways as a sum of consecutive naturals, for example, 1054 + ... + 1202.

It is an arithmetic number, because the mean of its divisors is an integer number (13500).

2¹⁶⁸⁰⁷² is an apocalyptic number.

168072 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 168072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (216000).

168072 is an abundant number, since it is smaller than the sum of its proper divisors (263928).

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

168072 is a wasteful number, since it uses less digits than its factorization.

168072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 205 (or 201 counting only the distinct ones).

The product of its (nonzero) digits is 672, while the sum is 24.

The square root of 168072 is about 409.9658522365. The cubic root of 168072 is about 55.1863650423.

The spelling of 168072 in words is "one hundred sixty-eight thousand, seventy-two".