82384646400 has 1080 divisors, whose sum is σ = 354033423744. Its totient is φ = 18513100800.

The previous prime is 82384646369. The next prime is 82384646411. The reversal of 82384646400 is 464648328.

82384646400 is a `hidden beast` number, since 8 + 238 + 4 + 6 + 4 + 6 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (1080).

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 119 ways as a sum of consecutive naturals, for example, 264902245 + ... + 264902555.

Almost surely, 2^82384646400 is an apocalyptic number.

82384646400 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 82384646400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (177016711872).

82384646400 is an abundant number, since it is smaller than the sum of its proper divisors (271648777344).

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

82384646400 is a wasteful number, since it uses less digits than its factorization.

82384646400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 429 (or 401 counting only the distinct ones).

The product of its (nonzero) digits is 884736, while the sum is 45.

The spelling of 82384646400 in words is "eighty-two billion, three hundred eighty-four million, six hundred forty-six thousand, four hundred".