72688 has 40 divisors (see below), whose sum is σ = 178560. Its totient is φ = 27840.

The previous prime is 72679. The next prime is 72689. The reversal of 72688 is 88627.

It is a Smith number, since the sum of its digits (31) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72689) by changing a digit.

72688 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, 1203 + ... + 1261.

It is an arithmetic number, because the mean of its divisors is an integer number (4464).

2⁷²⁶⁸⁸ 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 72688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (89280).

72688 is an abundant number, since it is smaller than the sum of its proper divisors (105872).

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

72688 is a wasteful number, since it uses less digits than its factorization.

72688 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 85 (or 79 counting only the distinct ones).

The product of its digits is 5376, while the sum is 31.

The square root of 72688 is about 269.6071215677. The cubic root of 72688 is about 41.7337656652.

The spelling of 72688 in words is "seventy-two thousand, six hundred eighty-eight".