82272682800 has 1920 divisors, whose sum is σ = 396774604800. Its totient is φ = 15676416000.

The previous prime is 82272682787. The next prime is 82272682801. The reversal of 82272682800 is 828627228.

It is a happy number.

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

It is not an unprimeable number, because it can be changed into a prime (82272682801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 647816337 + ... + 647816463.

It is an arithmetic number, because the mean of its divisors is an integer number (206653440).

Almost surely, 2^82272682800 is an apocalyptic number.

82272682800 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 82272682800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (198387302400).

82272682800 is an abundant number, since it is smaller than the sum of its proper divisors (314501922000).

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

82272682800 is a wasteful number, since it uses less digits than its factorization.

82272682800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 232 (or 215 counting only the distinct ones).

The product of its (nonzero) digits is 344064, while the sum is 45.

The spelling of 82272682800 in words is "eighty-two billion, two hundred seventy-two million, six hundred eighty-two thousand, eight hundred".