82517486400000 has 4800 divisors, whose sum is σ = 356472224317440. Its totient is φ = 18886348800000.

The previous prime is 82517486399879. The next prime is 82517486400001. The reversal of 82517486400000 is 468471528.

82517486400000 is a `hidden beast` number, since 82 + 51 + 7 + 486 + 40 + 0 + 0 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (4800).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82517486400001) by changing a digit.

It is a polite number, since it can be written in 479 ways as a sum of consecutive naturals, for example, 1755691199977 + ... + 1755691200023.

Almost surely, 2^{82517486400000} is an apocalyptic number.

82517486400000 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 82517486400000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (178236112158720).

82517486400000 is an abundant number, since it is smaller than the sum of its proper divisors (273954737917440).

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

82517486400000 is an equidigital number, since it uses as much as digits as its factorization.

82517486400000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 175 (or 130 counting only the distinct ones).

The product of its (nonzero) digits is 430080, while the sum is 45.

The spelling of 82517486400000 in words is "eighty-two trillion, five hundred seventeen billion, four hundred eighty-six million, four hundred thousand".