384944400 has 225 divisors, whose sum is σ = 1394325471. Its totient is φ = 101710080.

The previous prime is 384944383. The next prime is 384944401. The reversal of 384944400 is 4449483.

The square root of 384944400 is 19620.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 4 ways, for example, as 1411344 + 383533056 = 1188^2 + 19584^2 .

It is a tau number, because it is divible by the number of its divisors (225).

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

It is not an unprimeable number, because it can be changed into a prime (384944401) by changing a digit.

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 44 ways as a sum of consecutive naturals, for example, 3531546 + ... + 3531654.

Almost surely, 2^384944400 is an apocalyptic number.

384944400 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

384944400 is the 19620-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 384944400

384944400 is an abundant number, since it is smaller than the sum of its proper divisors (1009381071).

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

384944400 is a wasteful number, since it uses less digits than its factorization.

384944400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 248 (or 119 counting only the distinct ones).

The product of its (nonzero) digits is 55296, while the sum is 36.

The cubic root of 384944400 is about 727.4436134425.

Multiplying 384944400 by its sum of digits (36), we get a square (13857998400 = 117720²).

384944400 divided by its sum of digits (36) gives a square (10692900 = 3270²).

It can be divided in two parts, 384 and 944400, that added together give a square (944784 = 972²).

The spelling of 384944400 in words is "three hundred eighty-four million, nine hundred forty-four thousand, four hundred".