3504384000 has 720 divisors, whose sum is σ = 14145391260. Its totient is φ = 862617600.

The previous prime is 3504383941. The next prime is 3504384007. The reversal of 3504384000 is 4834053.

It is a happy number.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 6 ways, for example, as 153363456 + 3351020544 = 12384^2 + 57888^2 .

It is a tau number, because it is divible by the number of its divisors (720).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (3504384007) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 269567994 + ... + 269568006.

Almost surely, 2^3504384000 is an apocalyptic number.

3504384000 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 3504384000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7072695630).

3504384000 is an abundant number, since it is smaller than the sum of its proper divisors (10641007260).

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

3504384000 is an equidigital number, since it uses as much as digits as its factorization.

3504384000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 75 (or 23 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 27.

The square root of 3504384000 is about 59197.8377983521. The cubic root of 3504384000 is about 1518.9281455412.

Multiplying 3504384000 by its product of nonzero digits (5760), we get a square (20185251840000 = 4492800²).

3504384000 divided by its product of nonzero digits (5760) gives a square (608400 = 780²).

The spelling of 3504384000 in words is "three billion, five hundred four million, three hundred eighty-four thousand".