82352977149600 has 720 divisors, whose sum is σ = 316278105343200. Its totient is φ = 20795340625920.

The previous prime is 82352977149557. The next prime is 82352977149647. The reversal of 82352977149600 is 694177925328.

82352977149600 is a `hidden beast` number, since 8 + 2 + 3 + 5 + 2 + 9 + 7 + 7 + 14 + 9 + 600 = 666.

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

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 2879762502 + ... + 2879791098.

It is an arithmetic number, because the mean of its divisors is an integer number (439275146310).

It is a 1-persistent number, because it is pandigital, but 2⋅82352977149600 = 164705954299200 is not.

Almost surely, 2^{82352977149600} is an apocalyptic number.

82352977149600 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 82352977149600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (158139052671600).

82352977149600 is an abundant number, since it is smaller than the sum of its proper divisors (233925128193600).

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

82352977149600 is a wasteful number, since it uses less digits than its factorization.

82352977149600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 30987 (or 30965 counting only the distinct ones).

The product of its (nonzero) digits is 45722880, while the sum is 63.

The spelling of 82352977149600 in words is "eighty-two trillion, three hundred fifty-two billion, nine hundred seventy-seven million, one hundred forty-nine thousand, six hundred".