82711200 has 288 divisors, whose sum is σ = 317604672. Its totient is φ = 18432000.

The previous prime is 82711159. The next prime is 82711207. The reversal of 82711200 is 211728.

It is a super-2 number, since 2×82711200² = 13682285210880000, which contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82711207) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 343080 + ... + 343320.

It is an arithmetic number, because the mean of its divisors is an integer number (1102794).

Almost surely, 2^82711200 is an apocalyptic number.

82711200 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 82711200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (158802336).

82711200 is an abundant number, since it is smaller than the sum of its proper divisors (234893472).

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

82711200 is a wasteful number, since it uses less digits than its factorization.

82711200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 288 (or 275 counting only the distinct ones).

The product of its (nonzero) digits is 224, while the sum is 21.

The square root of 82711200 is about 9094.5698084077. The cubic root of 82711200 is about 435.7005490864.

Adding to 82711200 its reverse (211728), we get a palindrome (82922928).

The spelling of 82711200 in words is "eighty-two million, seven hundred eleven thousand, two hundred".