82035200 has 240 divisors, whose sum is σ = 239750280. Its totient is φ = 27525120.

The previous prime is 82035199. The next prime is 82035203. The reversal of 82035200 is 253028.

It can be written as a sum of positive squares in 12 ways, for example, as 3748096 + 78287104 = 1936^2 + 8848^2 .

It is a Harshad number since it is a multiple of its sum of digits (20).

It is not an unprimeable number, because it can be changed into a prime (82035203) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2828786 + ... + 2828814.

Almost surely, 2^82035200 is an apocalyptic number.

82035200 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 82035200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (119875140).

82035200 is an abundant number, since it is smaller than the sum of its proper divisors (157715080).

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

82035200 is a wasteful number, since it uses less digits than its factorization.

82035200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 87 (or 66 counting only the distinct ones).

The product of its (nonzero) digits is 480, while the sum is 20.

The square root of 82035200 is about 9057.3285244602. The cubic root of 82035200 is about 434.5103046222.

Adding to 82035200 its reverse (253028), we get a palindrome (82288228).

The spelling of 82035200 in words is "eighty-two million, thirty-five thousand, two hundred".