384964272 has 320 divisors, whose sum is σ = 1405624320. Its totient is φ = 97977600.

The previous prime is 384964267. The next prime is 384964273. The reversal of 384964272 is 272469483.

384964272 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a nude number because it is divisible by every one of its digits.

It is not an unprimeable number, because it can be changed into a prime (384964273) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 2361663 + ... + 2361825.

It is an arithmetic number, because the mean of its divisors is an integer number (4392576).

Almost surely, 2^384964272 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 384964272, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (702812160).

384964272 is an abundant number, since it is smaller than the sum of its proper divisors (1020660048).

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

384964272 is a wasteful number, since it uses less digits than its factorization.

384964272 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 269 (or 257 counting only the distinct ones).

The product of its digits is 580608, while the sum is 45.

The square root of 384964272 is about 19620.5064154828. The cubic root of 384964272 is about 727.4561308439.

It can be divided in two parts, 3849 and 64272, that added together give a square (68121 = 261²).

The spelling of 384964272 in words is "three hundred eighty-four million, nine hundred sixty-four thousand, two hundred seventy-two".