82416348172800 has 720 divisors, whose sum is σ = 297959866981920. Its totient is φ = 21753937920000.

The previous prime is 82416348172793. The next prime is 82416348172849. The reversal of 82416348172800 is 827184361428.

82416348172800 is a `hidden beast` number, since 8 + 2 + 4 + 1 + 6 + 348 + 17 + 280 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (720).

It is a super-2 number, since 2×82416348172800² (a number of 29 digits) contains 22 as substring.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 6051564391 + ... + 6051578009.

It is an arithmetic number, because the mean of its divisors is an integer number (413833148586).

Almost surely, 2^{82416348172800} is an apocalyptic number.

82416348172800 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 82416348172800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (148979933490960).

82416348172800 is an abundant number, since it is smaller than the sum of its proper divisors (215543518809120).

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

82416348172800 is a wasteful number, since it uses less digits than its factorization.

82416348172800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 14185 (or 14161 counting only the distinct ones).

The product of its (nonzero) digits is 4128768, while the sum is 54.

The spelling of 82416348172800 in words is "eighty-two trillion, four hundred sixteen billion, three hundred forty-eight million, one hundred seventy-two thousand, eight hundred".