72516384 has 120 divisors (see below), whose sum is σ = 216157788. Its totient is φ = 23846400.

The previous prime is 72516377. The next prime is 72516403. The reversal of 72516384 is 48361527.

It can be written as a sum of positive squares in 2 ways, for example, as 71571600 + 944784 = 8460^2 + 972^2 .

It is a super-3 number, since 3×72516384³ (a number of 25 digits) contains 333 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 261654 + ... + 261930.

Almost surely, 2^72516384 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 72516384, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (108078894).

72516384 is an abundant number, since it is smaller than the sum of its proper divisors (143641404).

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

72516384 is a wasteful number, since it uses less digits than its factorization.

72516384 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 400 (or 383 counting only the distinct ones).

The product of its digits is 40320, while the sum is 36.

The square root of 72516384 is about 8515.6552302216. The cubic root of 72516384 is about 417.0089537956.

It can be divided in two parts, 72516 and 384, that added together give a square (72900 = 270²).

The spelling of 72516384 in words is "seventy-two million, five hundred sixteen thousand, three hundred eighty-four".