72720 has 60 divisors (see below), whose sum is σ = 246636. Its totient is φ = 19200.

The previous prime is 72719. The next prime is 72727. The reversal of 72720 is 2727.

It can be written as a sum of positive squares in 2 ways, for example, as 51984 + 20736 = 228^2 + 144^2 .

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a junction number, because it is equal to n+sod(n) for n = 72693 and 72702.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72727) 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 11 ways as a sum of consecutive naturals, for example, 670 + ... + 770.

2⁷²⁷²⁰ 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 72720, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (123318).

72720 is an abundant number, since it is smaller than the sum of its proper divisors (173916).

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

72720 is a wasteful number, since it uses less digits than its factorization.

72720 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 120 (or 111 counting only the distinct ones).

The product of its (nonzero) digits is 196, while the sum is 18.

The square root of 72720 is about 269.6664606509. Note that the first 3 decimals coincide. The cubic root of 72720 is about 41.7398890261.

It can be divided in two parts, 727 and 20, that added together give a palindrome (747).

The spelling of 72720 in words is "seventy-two thousand, seven hundred twenty", and thus it is an iban number.