82947688286400 has 1680 divisors, whose sum is σ = 353082248164800. Its totient is φ = 18708397424640.

The previous prime is 82947688286371. The next prime is 82947688286413. The reversal of 82947688286400 is 468288674928.

82947688286400 is a `hidden beast` number, since 8 + 2 + 9 + 4 + 7 + 68 + 82 + 86 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (1680).

It is a Harshad number since it is a multiple of its sum of digits (72).

It is an unprimeable number.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 64350416956 + ... + 64350418244.

It is an arithmetic number, because the mean of its divisors is an integer number (210168004860).

Almost surely, 2^{82947688286400} is an apocalyptic number.

82947688286400 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 82947688286400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (176541124082400).

82947688286400 is an abundant number, since it is smaller than the sum of its proper divisors (270134559878400).

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

82947688286400 is a wasteful number, since it uses less digits than its factorization.

82947688286400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2216 (or 2192 counting only the distinct ones).

The product of its (nonzero) digits is 594542592, while the sum is 72.

The spelling of 82947688286400 in words is "eighty-two trillion, nine hundred forty-seven billion, six hundred eighty-eight million, two hundred eighty-six thousand, four hundred".