82800264960 has 864 divisors, whose sum is σ = 351578465280. Its totient is φ = 18074935296.

The previous prime is 82800264949. The next prime is 82800264971. The reversal of 82800264960 is 6946200828.

82800264960 is a `hidden beast` number, since 82 + 80 + 0 + 2 + 6 + 496 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (82800264949) and next prime (82800264971).

It is a tau number, because it is divible by the number of its divisors (864).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 127975357 + ... + 127976003.

It is an arithmetic number, because the mean of its divisors is an integer number (406919520).

Almost surely, 2^82800264960 is an apocalyptic number.

82800264960 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 82800264960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (175789232640).

82800264960 is an abundant number, since it is smaller than the sum of its proper divisors (268778200320).

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

82800264960 is a wasteful number, since it uses less digits than its factorization.

82800264960 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 730 (or 687 counting only the distinct ones).

The product of its (nonzero) digits is 331776, while the sum is 45.

The spelling of 82800264960 in words is "eighty-two billion, eight hundred million, two hundred sixty-four thousand, nine hundred sixty".