82804800 has 168 divisors, whose sum is σ = 292786816. Its totient is φ = 20367360.

The previous prime is 82804781. The next prime is 82804801. The reversal of 82804800 is 840828.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is not an unprimeable number, because it can be changed into a prime (82804801) 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, 61737 + ... + 63063.

Almost surely, 2^82804800 is an apocalyptic number.

82804800 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 82804800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (146393408).

82804800 is an abundant number, since it is smaller than the sum of its proper divisors (209982016).

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

82804800 is a wasteful number, since it uses less digits than its factorization.

82804800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1365 (or 1350 counting only the distinct ones).

The product of its (nonzero) digits is 4096, while the sum is 30.

The square root of 82804800 is about 9099.7142812288. The cubic root of 82804800 is about 435.8648404101.

The spelling of 82804800 in words is "eighty-two million, eight hundred four thousand, eight hundred".