7884464378400 has 720 divisors, whose sum is σ = 29266183485000. Its totient is φ = 2065106534400.

The previous prime is 7884464378303. The next prime is 7884464378407. The reversal of 7884464378400 is 48734644887.

7884464378400 is a `hidden beast` number, since 7 + 8 + 84 + 46 + 43 + 78 + 400 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 511219280016 + 7373245098384 = 714996^2 + 2715372^2 .

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

It is not an unprimeable number, because it can be changed into a prime (7884464378407) by changing a digit.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 4937046402 + ... + 4937047998.

Almost surely, 2^{7884464378400} 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 7884464378400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (14633091742500).

7884464378400 is an abundant number, since it is smaller than the sum of its proper divisors (21381719106600).

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

7884464378400 is a wasteful number, since it uses less digits than its factorization.

7884464378400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2939 (or 2917 counting only the distinct ones).

The product of its (nonzero) digits is 115605504, while the sum is 63.

The spelling of 7884464378400 in words is "seven trillion, eight hundred eighty-four billion, four hundred sixty-four million, three hundred seventy-eight thousand, four hundred".