72585072 has 210 divisors, whose sum is σ = 247210368. Its totient is φ = 20575296.

The previous prime is 72585067. The next prime is 72585109. The reversal of 72585072 is 27058527.

72585072 is a `hidden beast` number, since 7 + 2 + 585 + 0 + 72 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 41 ways as a sum of consecutive naturals, for example, 571473 + ... + 571599.

Almost surely, 2^72585072 is an apocalyptic number.

72585072 is a gapful number since it is divisible by the number (72) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72585072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (123605184).

72585072 is an abundant number, since it is smaller than the sum of its proper divisors (174625296).

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

72585072 is a wasteful number, since it uses less digits than its factorization.

72585072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 167 (or 139 counting only the distinct ones).

The product of its (nonzero) digits is 39200, while the sum is 36.

The square root of 72585072 is about 8519.6873182060. The cubic root of 72585072 is about 417.1405767955.

The spelling of 72585072 in words is "seventy-two million, five hundred eighty-five thousand, seventy-two".