72384768 has 108 divisors (see below), whose sum is σ = 211645980. Its totient is φ = 23789568.

The previous prime is 72384761. The next prime is 72384779. The reversal of 72384768 is 86748327.

It is a happy number.

It can be written as a sum of positive squares in 2 ways, for example, as 21233664 + 51151104 = 4608^2 + 7152^2 .

It is not an unprimeable number, because it can be changed into a prime (72384761) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 204880 + ... + 205232.

It is an arithmetic number, because the mean of its divisors is an integer number (1959685).

Almost surely, 2^72384768 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 72384768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (105822990).

72384768 is an abundant number, since it is smaller than the sum of its proper divisors (139261212).

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

72384768 is a wasteful number, since it uses less digits than its factorization.

72384768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 464 (or 447 counting only the distinct ones).

The product of its digits is 451584, while the sum is 45.

The square root of 72384768 is about 8507.9238360484. The cubic root of 72384768 is about 416.7565129627.

It can be divided in two parts, 723 and 84768, that added together give a triangular number (85491 = T₄₁₃).

The spelling of 72384768 in words is "seventy-two million, three hundred eighty-four thousand, seven hundred sixty-eight".