82405200 has 120 divisors (see below), whose sum is σ = 270279328. Its totient is φ = 21450240.

The previous prime is 82405163. The next prime is 82405207. The reversal of 82405200 is 250428.

It is a tau number, because it is divible by the number of its divisors (120).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82405207) by changing a digit.

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 23 ways as a sum of consecutive naturals, for example, 50802 + ... + 52398.

Almost surely, 2^82405200 is an apocalyptic number.

82405200 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 82405200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (135139664).

82405200 is an abundant number, since it is smaller than the sum of its proper divisors (187874128).

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

82405200 is a wasteful number, since it uses less digits than its factorization.

82405200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1661 (or 1650 counting only the distinct ones).

The product of its (nonzero) digits is 640, while the sum is 21.

The square root of 82405200 is about 9077.7309940315. The cubic root of 82405200 is about 435.1625763037.

Adding to 82405200 its reverse (250428), we get a palindrome (82655628).

The spelling of 82405200 in words is "eighty-two million, four hundred five thousand, two hundred".