82886821808400 has 675 divisors, whose sum is σ = 305955101909919. Its totient is φ = 21490037890560.

The previous prime is 82886821808369. The next prime is 82886821808407. The reversal of 82886821808400 is 480812868828.

The square root of 82886821808400 is 9104220.

It is a perfect power (a square), and thus also a powerful number.

82886821808400 is a `hidden beast` number, since 8 + 2 + 8 + 8 + 6 + 8 + 218 + 0 + 8 + 400 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 7868496247056 + 75018325561344 = 2805084^2 + 8661312^2 .

It is a tau number, because it is divible by the number of its divisors (675).

It is not an unprimeable number, because it can be changed into a prime (82886821808407) by changing a digit.

It is a polite number, since it can be written in 134 ways as a sum of consecutive naturals, for example, 60634104517 + ... + 60634105883.

Almost surely, 2^{82886821808400} is an apocalyptic number.

82886821808400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

82886821808400 is the 9104220-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82886821808400

82886821808400 is an abundant number, since it is smaller than the sum of its proper divisors (223068280101519).

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

82886821808400 is an equidigital number, since it uses as much as digits as its factorization.

82886821808400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2838 (or 1414 counting only the distinct ones).

The product of its (nonzero) digits is 25165824, while the sum is 63.

The spelling of 82886821808400 in words is "eighty-two trillion, eight hundred eighty-six billion, eight hundred twenty-one million, eight hundred eight thousand, four hundred".