82072800 has 108 divisors (see below), whose sum is σ = 289434600. Its totient is φ = 21884160.

The previous prime is 82072759. The next prime is 82072801. The reversal of 82072800 is 827028.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82072801) 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 17 ways as a sum of consecutive naturals, for example, 1501 + ... + 12899.

It is an arithmetic number, because the mean of its divisors is an integer number (2679950).

Almost surely, 2^82072800 is an apocalyptic number.

82072800 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 82072800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (144717300).

82072800 is an abundant number, since it is smaller than the sum of its proper divisors (207361800).

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

82072800 is a wasteful number, since it uses less digits than its factorization.

82072800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 11425 (or 11409 counting only the distinct ones).

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

The square root of 82072800 is about 9059.4039539034. The cubic root of 82072800 is about 434.5766789429.

Adding to 82072800 its reverse (827028), we get a palindrome (82899828).

The spelling of 82072800 in words is "eighty-two million, seventy-two thousand, eight hundred".