82688400 has 180 divisors, whose sum is σ = 291036928. Its totient is φ = 21738240.

The previous prime is 82688371. The next prime is 82688401. The reversal of 82688400 is 488628.

It is a tau number, because it is divible by the number of its divisors (180).

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

It is not an unprimeable number, because it can be changed into a prime (82688401) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 370689 + ... + 370911.

Almost surely, 2^82688400 is an apocalyptic number.

82688400 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 82688400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (145518464).

82688400 is an abundant number, since it is smaller than the sum of its proper divisors (208348528).

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

82688400 is a wasteful number, since it uses less digits than its factorization.

82688400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 350 (or 336 counting only the distinct ones).

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

The square root of 82688400 is about 9093.3162267679. The cubic root of 82688400 is about 435.6605106335.

The spelling of 82688400 in words is "eighty-two million, six hundred eighty-eight thousand, four hundred".