82742017881600 has 7560 divisors, whose sum is σ = 421546364149680. Its totient is φ = 15726580531200.

The previous prime is 82742017881539. The next prime is 82742017881617. The reversal of 82742017881600 is 618871024728.

82742017881600 is a `hidden beast` number, since 8 + 2 + 7 + 4 + 20 + 1 + 7 + 8 + 8 + 1 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (7560).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 755 ways as a sum of consecutive naturals, for example, 2853173030386 + ... + 2853173030414.

It is an arithmetic number, because the mean of its divisors is an integer number (55760101078).

Almost surely, 2^{82742017881600} is an apocalyptic number.

82742017881600 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 82742017881600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (210773182074840).

82742017881600 is an abundant number, since it is smaller than the sum of its proper divisors (338804346268080).

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

82742017881600 is a wasteful number, since it uses less digits than its factorization.

82742017881600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 142 (or 76 counting only the distinct ones).

The product of its (nonzero) digits is 2408448, while the sum is 54.

The spelling of 82742017881600 in words is "eighty-two trillion, seven hundred forty-two billion, seventeen million, eight hundred eighty-one thousand, six hundred".