72816 has 40 divisors (see below), whose sum is σ = 197904. Its totient is φ = 23040.

The previous prime is 72797. The next prime is 72817. The reversal of 72816 is 61827.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72817) by changing a digit.

72816 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1756 + ... + 1796.

2⁷²⁸¹⁶ 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 72816, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (98952).

72816 is an abundant number, since it is smaller than the sum of its proper divisors (125088).

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

72816 is a wasteful number, since it uses less digits than its factorization.

72816 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 89 (or 83 counting only the distinct ones).

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

The square root of 72816 is about 269.8443996084. The cubic root of 72816 is about 41.7582483374.

It can be divided in two parts, 72 and 816, that added together give a palindrome (888).

The spelling of 72816 in words is "seventy-two thousand, eight hundred sixteen".