82009014796800 has 4800 divisors, whose sum is σ = 388000487212800. Its totient is φ = 17065973514240.

The previous prime is 82009014796799. The next prime is 82009014796817. The reversal of 82009014796800 is 869741090028.

82009014796800 is a `hidden beast` number, since 8 + 2 + 0 + 0 + 90 + 1 + 479 + 6 + 80 + 0 = 666.

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

It is a super-2 number, since 2×82009014796800² (a number of 29 digits) contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 479 ways as a sum of consecutive naturals, for example, 1123411161564 + ... + 1123411161636.

It is an arithmetic number, because the mean of its divisors is an integer number (80833434836).

Almost surely, 2^{82009014796800} is an apocalyptic number.

82009014796800 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 82009014796800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (194000243606400).

82009014796800 is an abundant number, since it is smaller than the sum of its proper divisors (305991472416000).

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

82009014796800 is an frugal number, since it uses more digits than its factorization.

82009014796800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 162 (or 103 counting only the distinct ones).

The product of its (nonzero) digits is 1741824, while the sum is 54.

The spelling of 82009014796800 in words is "eighty-two trillion, nine billion, fourteen million, seven hundred ninety-six thousand, eight hundred".