72657 has 24 divisors (see below), whose sum is σ = 122304. Its totient is φ = 42768.

The previous prime is 72649. The next prime is 72661. The reversal of 72657 is 75627.

72657 is a `hidden beast` number, since 7 + 2 + 657 = 666.

It is not a de Polignac number, because 72657 - 2³ = 72649 is a prime.

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

It is a self number, because there is not a number n which added to its sum of digits gives 72657.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 72657.

It is not an unprimeable number, because it can be changed into a prime (72617) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 3148 + ... + 3170.

It is an arithmetic number, because the mean of its divisors is an integer number (5096).

2⁷²⁶⁵⁷ is an apocalyptic number.

It is an amenable number.

72657 is a deficient number, since it is larger than the sum of its proper divisors (49647).

72657 is a wasteful number, since it uses less digits than its factorization.

72657 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 51 (or 39 counting only the distinct ones).

The product of its digits is 2940, while the sum is 27.

The square root of 72657 is about 269.5496243737. The cubic root of 72657 is about 41.7278319453.

It can be divided in two parts, 72 and 657, that added together give a 6-th power (729 = 3⁶).

The spelling of 72657 in words is "seventy-two thousand, six hundred fifty-seven".