82582790400 has 1458 divisors, whose sum is σ = 353154913566. Its totient is φ = 18382848000.

The previous prime is 82582790393. The next prime is 82582790497. The reversal of 82582790400 is 409728528.

82582790400 is a `hidden beast` number, since 82 + 5 + 82 + 7 + 90 + 400 = 666.

It can be written as a sum of positive squares in 9 ways, for example, as 20474175744 + 62108614656 = 143088^2 + 249216^2 .

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 pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 161 ways as a sum of consecutive naturals, for example, 2014214380 + ... + 2014214420.

Almost surely, 2^82582790400 is an apocalyptic number.

82582790400 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 82582790400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (176577456783).

82582790400 is an abundant number, since it is smaller than the sum of its proper divisors (270572123166).

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

82582790400 is a wasteful number, since it uses less digits than its factorization.

82582790400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 129 (or 79 counting only the distinct ones).

The product of its (nonzero) digits is 322560, while the sum is 45.

The spelling of 82582790400 in words is "eighty-two billion, five hundred eighty-two million, seven hundred ninety thousand, four hundred".