82290307276800 has 2688 divisors, whose sum is σ = 370700159385600. Its totient is φ = 17467661352960.

The previous prime is 82290307276781. The next prime is 82290307276819. The reversal of 82290307276800 is 867270309228.

82290307276800 is a `hidden beast` number, since 8 + 2 + 290 + 3 + 0 + 7 + 276 + 80 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (82290307276781) and next prime (82290307276819).

It is a tau number, because it is divible by the number of its divisors (2688).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

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 191 ways as a sum of consecutive naturals, for example, 51983768809 + ... + 51983770391.

Almost surely, 2^{82290307276800} is an apocalyptic number.

82290307276800 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 82290307276800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (185350079692800).

82290307276800 is an abundant number, since it is smaller than the sum of its proper divisors (288409852108800).

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

82290307276800 is a wasteful number, since it uses less digits than its factorization.

82290307276800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1731 (or 1696 counting only the distinct ones).

The product of its (nonzero) digits is 4064256, while the sum is 54.

The spelling of 82290307276800 in words is "eighty-two trillion, two hundred ninety billion, three hundred seven million, two hundred seventy-six thousand, eight hundred".