82317312000 has 1536 divisors, whose sum is σ = 382766342400. Its totient is φ = 16515072000.

The previous prime is 82317311983. The next prime is 82317312013. The reversal of 82317312000 is 21371328.

It is a tau number, because it is divible by the number of its divisors (1536).

It is a super-2 number, since 2×82317312000² (a number of 23 digits) contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 2838527986 + ... + 2838528014.

Almost surely, 2^82317312000 is an apocalyptic number.

82317312000 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 82317312000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (191383171200).

82317312000 is an abundant number, since it is smaller than the sum of its proper divisors (300449030400).

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

82317312000 is a wasteful number, since it uses less digits than its factorization.

82317312000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 98 (or 57 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 27.

Adding to 82317312000 its reverse (21371328), we get a palindrome (82338683328).

The spelling of 82317312000 in words is "eighty-two billion, three hundred seventeen million, three hundred twelve thousand".