82731716496000 has 3840 divisors, whose sum is σ = 379004463002880. Its totient is φ = 17696600064000.

The previous prime is 82731716495929. The next prime is 82731716496007. The reversal of 82731716496000 is 69461713728.

82731716496000 is a `hidden beast` number, since 8 + 2 + 7 + 3 + 17 + 16 + 4 + 9 + 600 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is not an unprimeable number, because it can be changed into a prime (82731716496007) 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, 55413071254 + ... + 55413072746.

It is an arithmetic number, because the mean of its divisors is an integer number (98699078907).

Almost surely, 2^{82731716496000} is an apocalyptic number.

82731716496000 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 82731716496000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (189502231501440).

82731716496000 is an abundant number, since it is smaller than the sum of its proper divisors (296272746506880).

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

82731716496000 is a wasteful number, since it uses less digits than its factorization.

82731716496000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1594 (or 1550 counting only the distinct ones).

The product of its (nonzero) digits is 3048192, while the sum is 54.

The spelling of 82731716496000 in words is "eighty-two trillion, seven hundred thirty-one billion, seven hundred sixteen million, four hundred ninety-six thousand".