82822972800 has 768 divisors, whose sum is σ = 295052544000. Its totient is φ = 20383334400.

The previous prime is 82822972777. The next prime is 82822972801. The reversal of 82822972800 is 827922828.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a self number, because there is not a number n which added to its sum of digits gives 82822972800.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82822972801) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 930595156 + ... + 930595244.

It is an arithmetic number, because the mean of its divisors is an integer number (384183000).

Almost surely, 2^82822972800 is an apocalyptic number.

82822972800 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 82822972800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (147526272000).

82822972800 is an abundant number, since it is smaller than the sum of its proper divisors (212229571200).

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

82822972800 is a wasteful number, since it uses less digits than its factorization.

82822972800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 259 (or 242 counting only the distinct ones).

The product of its (nonzero) digits is 516096, while the sum is 48.

The spelling of 82822972800 in words is "eighty-two billion, eight hundred twenty-two million, nine hundred seventy-two thousand, eight hundred".