82807200 has 432 divisors, whose sum is σ = 350977536. Its totient is φ = 17971200.

The previous prime is 82807181. The next prime is 82807213. The reversal of 82807200 is 270828.

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 71 ways as a sum of consecutive naturals, for example, 1562374 + ... + 1562426.

It is an arithmetic number, because the mean of its divisors is an integer number (812448).

Almost surely, 2^82807200 is an apocalyptic number.

82807200 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 82807200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (175488768).

82807200 is an abundant number, since it is smaller than the sum of its proper divisors (268170336).

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

82807200 is a wasteful number, since it uses less digits than its factorization.

82807200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 117 (or 101 counting only the distinct ones).

The product of its (nonzero) digits is 1792, while the sum is 27.

The square root of 82807200 is about 9099.8461525457. The cubic root of 82807200 is about 435.8690513798.

The spelling of 82807200 in words is "eighty-two million, eight hundred seven thousand, two hundred".