82168967384100 has 1215 divisors, whose sum is σ = 291704775097281. Its totient is φ = 20088847713600.

The previous prime is 82168967384039. The next prime is 82168967384129. The reversal of 82168967384100 is 148376986128.

The square root of 82168967384100 is 9064710.

It is a perfect power (a square), and thus also a powerful number.

82168967384100 is a `hidden beast` number, since 8 + 2 + 1 + 68 + 96 + 7 + 384 + 100 = 666.

It can be written as a sum of positive squares in only one way, i.e., 29580828258276 + 52588139125824 = 5438826^2 + 7251768^2 .

It is a tau number, because it is divible by the number of its divisors (1215).

It is an unprimeable number.

It is a polite number, since it can be written in 404 ways as a sum of consecutive naturals, for example, 2650611851085 + ... + 2650611851115.

Almost surely, 2^{82168967384100} is an apocalyptic number.

82168967384100 is the 9064710-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82168967384100

82168967384100 is an abundant number, since it is smaller than the sum of its proper divisors (209535807713181).

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

82168967384100 is an frugal number, since it uses more digits than its factorization.

82168967384100 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 176 (or 60 counting only the distinct ones).

The product of its (nonzero) digits is 27869184, while the sum is 63.

The spelling of 82168967384100 in words is "eighty-two trillion, one hundred sixty-eight billion, nine hundred sixty-seven million, three hundred eighty-four thousand, one hundred".