82375200 has 216 divisors, whose sum is σ = 308019348. Its totient is φ = 20643840.

The previous prime is 82375169. The next prime is 82375201. The reversal of 82375200 is 257328.

It can be written as a sum of positive squares in 6 ways, for example, as 34433424 + 47941776 = 5868^2 + 6924^2 .

It is not an unprimeable number, because it can be changed into a prime (82375201) 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 35 ways as a sum of consecutive naturals, for example, 122064 + ... + 122736.

Almost surely, 2^82375200 is an apocalyptic number.

82375200 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 82375200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (154009674).

82375200 is an abundant number, since it is smaller than the sum of its proper divisors (225644148).

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

82375200 is a wasteful number, since it uses less digits than its factorization.

82375200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 716 (or 700 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 27.

The square root of 82375200 is about 9076.0784483168. The cubic root of 82375200 is about 435.1097622343.

The spelling of 82375200 in words is "eighty-two million, three hundred seventy-five thousand, two hundred".