82931200 has 240 divisors, whose sum is σ = 243555840. Its totient is φ = 27648000.

The previous prime is 82931197. The next prime is 82931207. The reversal of 82931200 is 213928.

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82931207) 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 23 ways as a sum of consecutive naturals, for example, 2675185 + ... + 2675215.

It is an arithmetic number, because the mean of its divisors is an integer number (1014816).

Almost surely, 2^82931200 is an apocalyptic number.

82931200 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 82931200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (121777920).

82931200 is an abundant number, since it is smaller than the sum of its proper divisors (160624640).

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

82931200 is a wasteful number, since it uses less digits than its factorization.

82931200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 89 (or 68 counting only the distinct ones).

The product of its (nonzero) digits is 864, while the sum is 25.

The square root of 82931200 is about 9106.6569058025. The cubic root of 82931200 is about 436.0865075381.

The spelling of 82931200 in words is "eighty-two million, nine hundred thirty-one thousand, two hundred".