82705924800 has 1176 divisors, whose sum is σ = 333992591856. Its totient is φ = 20065812480.

The previous prime is 82705924799. The next prime is 82705924823. The reversal of 82705924800 is 842950728.

82705924800 is a `hidden beast` number, since 82 + 7 + 0 + 5 + 92 + 480 + 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, 852638352 + ... + 852638448.

It is an arithmetic number, because the mean of its divisors is an integer number (284007306).

Almost surely, 2^82705924800 is an apocalyptic number.

82705924800 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 82705924800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (166996295928).

82705924800 is an abundant number, since it is smaller than the sum of its proper divisors (251286667056).

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

82705924800 is a wasteful number, since it uses less digits than its factorization.

82705924800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 197 (or 167 counting only the distinct ones).

The product of its (nonzero) digits is 322560, while the sum is 45.

The spelling of 82705924800 in words is "eighty-two billion, seven hundred five million, nine hundred twenty-four thousand, eight hundred".