82172306422800 has 840 divisors, whose sum is σ = 323943705079488. Its totient is φ = 19856264832000.

The previous prime is 82172306422741. The next prime is 82172306422847. The reversal of 82172306422800 is 822460327128.

82172306422800 is a `hidden beast` number, since 8 + 21 + 7 + 2 + 306 + 42 + 280 + 0 = 666.

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

It is an unprimeable number.

It is a polite number, since it can be written in 167 ways as a sum of consecutive naturals, for example, 997522414 + ... + 997604786.

Almost surely, 2^{82172306422800} is an apocalyptic number.

82172306422800 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 82172306422800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (161971852539744).

82172306422800 is an abundant number, since it is smaller than the sum of its proper divisors (241771398656688).

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

82172306422800 is a wasteful number, since it uses less digits than its factorization.

82172306422800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 82731 (or 82705 counting only the distinct ones).

The product of its (nonzero) digits is 516096, while the sum is 45.

Adding to 82172306422800 its reverse (822460327128), we get a palindrome (82994766749928).

The spelling of 82172306422800 in words is "eighty-two trillion, one hundred seventy-two billion, three hundred six million, four hundred twenty-two thousand, eight hundred".