82100800 has 126 divisors (see below), whose sum is σ = 213361778. Its totient is φ = 31088640.

The previous prime is 82100797. The next prime is 82100813. The reversal of 82100800 is 800128.

It is a happy number.

It can be written as a sum of positive squares in 3 ways, for example, as 4096576 + 78004224 = 2024^2 + 8832^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 846352 + ... + 846448.

Almost surely, 2^82100800 is an apocalyptic number.

82100800 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 82100800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (106680889).

82100800 is an abundant number, since it is smaller than the sum of its proper divisors (131260978).

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

82100800 is a wasteful number, since it uses less digits than its factorization.

82100800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 165 (or 127 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 19.

The square root of 82100800 is about 9060.9491776524. The cubic root of 82100800 is about 434.6260934607.

Adding to 82100800 its reverse (800128), we get a palindrome (82900928).

The spelling of 82100800 in words is "eighty-two million, one hundred thousand, eight hundred".