82200384000 has 1920 divisors, whose sum is σ = 378415065600. Its totient is φ = 16721510400.

The previous prime is 82200383989. The next prime is 82200384031. The reversal of 82200384000 is 48300228.

82200384000 is a `hidden beast` number, since 8 + 220 + 0 + 38 + 400 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1920).

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 2221631982 + ... + 2221632018.

It is an arithmetic number, because the mean of its divisors is an integer number (197091180).

Almost surely, 2^82200384000 is an apocalyptic number.

82200384000 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 82200384000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (189207532800).

82200384000 is an abundant number, since it is smaller than the sum of its proper divisors (296214681600).

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

82200384000 is a wasteful number, since it uses less digits than its factorization.

82200384000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 131 (or 102 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

Adding to 82200384000 its reverse (48300228), we get a palindrome (82248684228).

The spelling of 82200384000 in words is "eighty-two billion, two hundred million, three hundred eighty-four thousand".