72168 has 32 divisors (see below), whose sum is σ = 188160. Its totient is φ = 23040.

The previous prime is 72167. The next prime is 72169. The reversal of 72168 is 86127.

It is an interprime number because it is at equal distance from previous prime (72167) and next prime (72169).

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

It is a d-powerful number, because it can be written as 7⁵ + 2¹³ + 1 + 6⁶ + 8³ .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72161) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 696 + ... + 792.

It is an arithmetic number, because the mean of its divisors is an integer number (5880).

2⁷²¹⁶⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72168, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (94080).

72168 is an abundant number, since it is smaller than the sum of its proper divisors (115992).

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

72168 is a wasteful number, since it uses less digits than its factorization.

72168 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 137 (or 133 counting only the distinct ones).

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

The square root of 72168 is about 268.6410244173. The cubic root of 72168 is about 41.6340081866.

The spelling of 72168 in words is "seventy-two thousand, one hundred sixty-eight".