72960 has 72 divisors (see below), whose sum is σ = 245280. Its totient is φ = 18432.

The previous prime is 72959. The next prime is 72973. The reversal of 72960 is 6927.

72960 = 86² + 87² + ... + 94².

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

It is a self number, because there is not a number n which added to its sum of digits gives 72960.

It is a congruent number.

It is an unprimeable 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 7 ways as a sum of consecutive naturals, for example, 3831 + ... + 3849.

2⁷²⁹⁶⁰ 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 72960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (122640).

72960 is an abundant number, since it is smaller than the sum of its proper divisors (172320).

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

72960 is a wasteful number, since it uses less digits than its factorization.

72960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 43 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 756, while the sum is 24.

The square root of 72960 is about 270.1110882581. Note that the first 3 decimals coincide. The cubic root of 72960 is about 41.7857570729.

The spelling of 72960 in words is "seventy-two thousand, nine hundred sixty".