72384000 has 320 divisors, whose sum is σ = 268107840. Its totient is φ = 17203200.

The previous prime is 72383981. The next prime is 72384001. The reversal of 72384000 is 48327.

It is a tau number, because it is divible by the number of its divisors (320).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72384001) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 2495986 + ... + 2496014.

It is an arithmetic number, because the mean of its divisors is an integer number (837837).

Almost surely, 2^72384000 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 72384000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (134053920).

72384000 is an abundant number, since it is smaller than the sum of its proper divisors (195723840).

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

72384000 is a wasteful number, since it uses less digits than its factorization.

72384000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 78 (or 52 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 24.

The square root of 72384000 is about 8507.8787015331. The cubic root of 72384000 is about 416.7550390332.

The spelling of 72384000 in words is "seventy-two million, three hundred eighty-four thousand".