82212441292800 has 4104 divisors, whose sum is σ = 392305406534496. Its totient is φ = 16017543659520.

The previous prime is 82212441292763. The next prime is 82212441292801. The reversal of 82212441292800 is 829214421228.

It is a happy number.

82212441292800 is a `hidden beast` number, since 8 + 2 + 2 + 1 + 244 + 129 + 280 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82212441292801) by changing a digit.

It is a polite number, since it can be written in 215 ways as a sum of consecutive naturals, for example, 1551178137574 + ... + 1551178137626.

Almost surely, 2^{82212441292800} is an apocalyptic number.

82212441292800 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 82212441292800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (196152703267248).

82212441292800 is an abundant number, since it is smaller than the sum of its proper divisors (310092965241696).

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

82212441292800 is a wasteful number, since it uses less digits than its factorization.

82212441292800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 159 (or 100 counting only the distinct ones).

The product of its (nonzero) digits is 294912, while the sum is 45.

The spelling of 82212441292800 in words is "eighty-two trillion, two hundred twelve billion, four hundred forty-one million, two hundred ninety-two thousand, eight hundred".