82132358400 has 864 divisors, whose sum is σ = 324099256320. Its totient is φ = 20278149120.

The previous prime is 82132358351. The next prime is 82132358419. The reversal of 82132358400 is 485323128.

82132358400 is a `hidden beast` number, since 8 + 2 + 13 + 235 + 8 + 400 = 666.

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 (36).

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, 214444609 + ... + 214444991.

It is an arithmetic number, because the mean of its divisors is an integer number (375114880).

Almost surely, 2^82132358400 is an apocalyptic number.

82132358400 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 82132358400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (162049628160).

82132358400 is an abundant number, since it is smaller than the sum of its proper divisors (241966897920).

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

82132358400 is a wasteful number, since it uses less digits than its factorization.

82132358400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 508 (or 483 counting only the distinct ones).

The product of its (nonzero) digits is 46080, while the sum is 36.

The spelling of 82132358400 in words is "eighty-two billion, one hundred thirty-two million, three hundred fifty-eight thousand, four hundred".