84687782400 has 720 divisors, whose sum is σ = 329198445576. Its totient is φ = 20667432960.

The previous prime is 84687782383. The next prime is 84687782407. The reversal of 84687782400 is 428778648.

It is a happy number.

84687782400 is a `hidden beast` number, since 84 + 6 + 87 + 7 + 82 + 400 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 3202654464 + 81485127936 = 56592^2 + 285456^2 .

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 (84687782407) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 289036654 + ... + 289036946.

Almost surely, 2^84687782400 is an apocalyptic number.

84687782400 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 84687782400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (164599222788).

84687782400 is an abundant number, since it is smaller than the sum of its proper divisors (244510663176).

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

84687782400 is a wasteful number, since it uses less digits than its factorization.

84687782400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 533 (or 509 counting only the distinct ones).

The product of its (nonzero) digits is 4816896, while the sum is 54.

The spelling of 84687782400 in words is "eighty-four billion, six hundred eighty-seven million, seven hundred eighty-two thousand, four hundred".