82083600 has 135 divisors (see below), whose sum is σ = 286751829. Its totient is φ = 21744000.

The previous prime is 82083593. The next prime is 82083611. The reversal of 82083600 is 638028.

The square root of 82083600 is 9060.

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

It can be written as a sum of positive squares in only one way, i.e., 29550096 + 52533504 = 5436^2 + 7248^2 .

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 26 ways as a sum of consecutive naturals, for example, 543525 + ... + 543675.

Almost surely, 2^82083600 is an apocalyptic number.

82083600 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

82083600 is the 9060-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82083600

82083600 is an abundant number, since it is smaller than the sum of its proper divisors (204668229).

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

82083600 is a wasteful number, since it uses less digits than its factorization.

82083600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 326 (or 161 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The cubic root of 82083600 is about 434.5957401596.

Multiplying 82083600 by its product of nonzero digits (2304), we get a square (189120614400 = 434880²).

The spelling of 82083600 in words is "eighty-two million, eighty-three thousand, six hundred".