82305738207000 has 2304 divisors, whose sum is σ = 365292607680000. Its totient is φ = 16515539712000.

The previous prime is 82305738206947. The next prime is 82305738207013. The reversal of 82305738207000 is 70283750328.

82305738207000 is a `hidden beast` number, since 8 + 2 + 3 + 0 + 573 + 8 + 2 + 0 + 70 + 0 + 0 = 666.

82305738207000 is digitally balanced in base 4, because in such base it contains all the possibile digits an equal number of times.

It is a Cunningham number, because it is equal to 9072251²-1.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 575 ways as a sum of consecutive naturals, for example, 24948691351 + ... + 24948694649.

It is an arithmetic number, because the mean of its divisors is an integer number (158547138750).

Almost surely, 2^{82305738207000} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82305738207000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (182646303840000).

82305738207000 is an abundant number, since it is smaller than the sum of its proper divisors (282986869473000).

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

82305738207000 is a wasteful number, since it uses less digits than its factorization.

82305738207000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3527 (or 3503 counting only the distinct ones).

The product of its (nonzero) digits is 564480, while the sum is 45.

The spelling of 82305738207000 in words is "eighty-two trillion, three hundred five billion, seven hundred thirty-eight million, two hundred seven thousand".