72320 has 32 divisors (see below), whose sum is σ = 174420. Its totient is φ = 28672.

The previous prime is 72313. The next prime is 72337. The reversal of 72320 is 2327.

It can be written as a sum of positive squares in 2 ways, for example, as 61504 + 10816 = 248^2 + 104^2 .

It is a tau number, because it is divible by the number of its divisors (32).

It is a junction number, because it is equal to n+sod(n) for n = 72295 and 72304.

It is an unprimeable number.

72320 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 (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 584 + ... + 696.

2⁷²³²⁰ 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 72320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (87210).

72320 is an abundant number, since it is smaller than the sum of its proper divisors (102100).

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

72320 is a wasteful number, since it uses less digits than its factorization.

72320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 132 (or 120 counting only the distinct ones).

The product of its (nonzero) digits is 84, while the sum is 14.

The square root of 72320 is about 268.9237810235. The cubic root of 72320 is about 41.6632174923.

Adding to 72320 its reverse (2327), we get a palindrome (74647).

The spelling of 72320 in words is "seventy-two thousand, three hundred twenty", and thus it is an iban number.