72972 has 18 divisors (see below), whose sum is σ = 184548. Its totient is φ = 24312.

The previous prime is 72959. The next prime is 72973. The reversal of 72972 is 27927.

It is a tau number, because it is divible by the number of its divisors (18).

It is an Ulam number.

72972 is a modest number, since divided by 972 gives 72 as remainder.

It is not an unprimeable number, because it can be changed into a prime (72973) by changing a digit.

72972 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 5 ways as a sum of consecutive naturals, for example, 978 + ... + 1049.

2⁷²⁹⁷² is an apocalyptic number.

It is an amenable number.

72972 is an abundant number, since it is smaller than the sum of its proper divisors (111576).

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

72972 is a wasteful number, since it uses less digits than its factorization.

72972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2037 (or 2032 counting only the distinct ones).

The product of its digits is 1764, while the sum is 27.

The square root of 72972 is about 270.1333004278. The cubic root of 72972 is about 41.7880478331.

The spelling of 72972 in words is "seventy-two thousand, nine hundred seventy-two".