72009 has 20 divisors (see below), whose sum is σ = 123904. Its totient is φ = 40824.

The previous prime is 71999. The next prime is 72019. The reversal of 72009 is 90027.

It is an interprime number because it is at equal distance from previous prime (71999) and next prime (72019).

It is not a de Polignac number, because 72009 - 2⁴ = 71993 is a prime.

It is a Duffinian number.

It is a junction number, because it is equal to n+sod(n) for n = 71982 and 72000.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72019) by changing a digit.

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 19 ways as a sum of consecutive naturals, for example, 504 + ... + 630.

2⁷²⁰⁰⁹ is an apocalyptic number.

It is an amenable number.

72009 is a deficient number, since it is larger than the sum of its proper divisors (51895).

72009 is a wasteful number, since it uses less digits than its factorization.

72009 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 146 (or 137 counting only the distinct ones).

The product of its (nonzero) digits is 126, while the sum is 18.

The square root of 72009 is about 268.3449272858. The cubic root of 72009 is about 41.6034097920.

Adding to 72009 its sum of digits (18), we get a palindrome (72027).

It can be divided in two parts, 7 and 2009, that added together give a triangular number (2016 = T₆₃).

The spelling of 72009 in words is "seventy-two thousand, nine".