82601164800 has 1440 divisors, whose sum is σ = 382257200640. Its totient is φ = 16986931200.

The previous prime is 82601164733. The next prime is 82601164801. The reversal of 82601164800 is 846110628.

82601164800 is a `hidden beast` number, since 8 + 2 + 6 + 0 + 1 + 1 + 648 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1440).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82601164801) 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, 851558352 + ... + 851558448.

Almost surely, 2^82601164800 is an apocalyptic number.

82601164800 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 82601164800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (191128600320).

82601164800 is an abundant number, since it is smaller than the sum of its proper divisors (299656035840).

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

82601164800 is a wasteful number, since it uses less digits than its factorization.

82601164800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 162 (or 125 counting only the distinct ones).

The product of its (nonzero) digits is 18432, while the sum is 36.

The spelling of 82601164800 in words is "eighty-two billion, six hundred one million, one hundred sixty-four thousand, eight hundred".