3984364800 has 648 divisors, whose sum is σ = 16295066424. Its totient is φ = 920125440.

The previous prime is 3984364757. The next prime is 3984364823. The reversal of 3984364800 is 84634893.

It can be written as a sum of positive squares in 12 ways, for example, as 2579014656 + 1405350144 = 50784^2 + 37488^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 12729444 + ... + 12729756.

Almost surely, 2^3984364800 is an apocalyptic number.

3984364800 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 3984364800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8147533212).

3984364800 is an abundant number, since it is smaller than the sum of its proper divisors (12310701624).

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

3984364800 is a wasteful number, since it uses less digits than its factorization.

3984364800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 375 (or 353 counting only the distinct ones).

The product of its (nonzero) digits is 497664, while the sum is 45.

The square root of 3984364800 is about 63121.8250686718. The cubic root of 3984364800 is about 1585.3300735289.

The spelling of 3984364800 in words is "three billion, nine hundred eighty-four million, three hundred sixty-four thousand, eight hundred".