72765 has 48 divisors (see below), whose sum is σ = 164160. Its totient is φ = 30240.

The previous prime is 72763. The next prime is 72767. The reversal of 72765 is 56727.

It is an interprime number because it is at equal distance from previous prime (72763) and next prime (72767).

It is not a de Polignac number, because 72765 - 2¹ = 72763 is a prime.

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

It is an alternating number because its digits alternate between odd and even.

It is a Curzon number.

72765 is a lucky number.

It is a nialpdrome in base 7.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 72765.

It is not an unprimeable number, because it can be changed into a prime (72763) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 6610 + ... + 6620.

It is an arithmetic number, because the mean of its divisors is an integer number (3420).

2⁷²⁷⁶⁵ is an apocalyptic number.

It is an amenable number.

72765 is an abundant number, since it is smaller than the sum of its proper divisors (91395).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (82080).

72765 is a wasteful number, since it uses less digits than its factorization.

72765 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 39 (or 26 counting only the distinct ones).

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

The square root of 72765 is about 269.7498841520. The cubic root of 72765 is about 41.7484969638.

It can be divided in two parts, 7 and 2765, that added together give a palindrome (2772).

The spelling of 72765 in words is "seventy-two thousand, seven hundred sixty-five".