72585672 has 64 divisors (see below), whose sum is σ = 186796800. Its totient is φ = 23493120.

The previous prime is 72585671. The next prime is 72585683. The reversal of 72585672 is 27658527.

It is an alternating number because its digits alternate between odd and even.

It is not an unprimeable number, because it can be changed into a prime (72585671) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 258172 + ... + 258452.

It is an arithmetic number, because the mean of its divisors is an integer number (2918700).

Almost surely, 2^72585672 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 72585672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (93398400).

72585672 is an abundant number, since it is smaller than the sum of its proper divisors (114211128).

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

72585672 is a wasteful number, since it uses less digits than its factorization.

72585672 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 566 (or 562 counting only the distinct ones).

The product of its digits is 235200, while the sum is 42.

The square root of 72585672 is about 8519.7225306931. The cubic root of 72585672 is about 417.1417261762.

The spelling of 72585672 in words is "seventy-two million, five hundred eighty-five thousand, six hundred seventy-two".