84689440358400 has 3600 divisors, whose sum is σ = 350438189270400. Its totient is φ = 20143103016960.

The previous prime is 84689440358363. The next prime is 84689440358407. The reversal of 84689440358400 is 485304498648.

84689440358400 is a `hidden beast` number, since 8 + 4 + 6 + 8 + 9 + 4 + 40 + 3 + 584 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (3600).

It is not an unprimeable number, because it can be changed into a prime (84689440358407) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 951566745556 + ... + 951566745644.

It is an arithmetic number, because the mean of its divisors is an integer number (97343941464).

Almost surely, 2^{84689440358400} is an apocalyptic number.

84689440358400 is a gapful number since it is divisible by the number (80) 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 84689440358400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (175219094635200).

84689440358400 is an abundant number, since it is smaller than the sum of its proper divisors (265748748912000).

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

84689440358400 is a wasteful number, since it uses less digits than its factorization.

84689440358400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 234 (or 194 counting only the distinct ones).

The product of its (nonzero) digits is 106168320, while the sum is 63.

The spelling of 84689440358400 in words is "eighty-four trillion, six hundred eighty-nine billion, four hundred forty million, three hundred fifty-eight thousand, four hundred".