82303645132800 has 5184 divisors, whose sum is σ = 392929003434240. Its totient is φ = 16284521594880.

The previous prime is 82303645132763. The next prime is 82303645132901. The reversal of 82303645132800 is 823154630328.

82303645132800 is a `hidden beast` number, since 8 + 2 + 3 + 0 + 364 + 5 + 1 + 3 + 280 + 0 = 666.

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 431 ways as a sum of consecutive naturals, for example, 492836198317 + ... + 492836198483.

It is an arithmetic number, because the mean of its divisors is an integer number (75796489860).

Almost surely, 2^{82303645132800} is an apocalyptic number.

82303645132800 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 82303645132800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (196464501717120).

82303645132800 is an abundant number, since it is smaller than the sum of its proper divisors (310625358301440).

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

82303645132800 is a wasteful number, since it uses less digits than its factorization.

82303645132800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 328 (or 293 counting only the distinct ones).

The product of its (nonzero) digits is 829440, while the sum is 45.

The spelling of 82303645132800 in words is "eighty-two trillion, three hundred three billion, six hundred forty-five million, one hundred thirty-two thousand, eight hundred".