72768 has 28 divisors (see below), whose sum is σ = 193040. Its totient is φ = 24192.

The previous prime is 72767. The next prime is 72797. The reversal of 72768 is 86727.

It is not an unprimeable number, because it can be changed into a prime (72763) 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 3 ways as a sum of consecutive naturals, for example, 3 + ... + 381.

2⁷²⁷⁶⁸ 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 72768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (96520).

72768 is an abundant number, since it is smaller than the sum of its proper divisors (120272).

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

72768 is a wasteful number, since it uses less digits than its factorization.

72768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 394 (or 384 counting only the distinct ones).

The product of its digits is 4704, while the sum is 30.

The square root of 72768 is about 269.7554448014. The cubic root of 72768 is about 41.7490707001.

It can be divided in two parts, 7 and 2768, that added together give a triangular number (2775 = T₇₄).

The spelling of 72768 in words is "seventy-two thousand, seven hundred sixty-eight".