82684800 has 480 divisors, whose sum is σ = 344341800. Its totient is φ = 19353600.

The previous prime is 82684769. The next prime is 82684807. The reversal of 82684800 is 848628.

It is a tau number, because it is divible by the number of its divisors (480).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82684807) 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 59 ways as a sum of consecutive naturals, for example, 2851186 + ... + 2851214.

Almost surely, 2^82684800 is an apocalyptic number.

82684800 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 82684800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (172170900).

82684800 is an abundant number, since it is smaller than the sum of its proper divisors (261657000).

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

82684800 is a wasteful number, since it uses less digits than its factorization.

82684800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 76 (or 50 counting only the distinct ones).

The product of its (nonzero) digits is 24576, while the sum is 36.

The square root of 82684800 is about 9093.1182770269. The cubic root of 82684800 is about 435.6541880998.

The spelling of 82684800 in words is "eighty-two million, six hundred eighty-four thousand, eight hundred".