82303200 has 432 divisors, whose sum is σ = 350977536. Its totient is φ = 17740800.

The previous prime is 82303181. The next prime is 82303201. The reversal of 82303200 is 230328.

82303200 = 165³ + 166³ + ... + 180³.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82303201) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 1159165 + ... + 1159235.

It is an arithmetic number, because the mean of its divisors is an integer number (812448).

Almost surely, 2^82303200 is an apocalyptic number.

82303200 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 82303200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (175488768).

82303200 is an abundant number, since it is smaller than the sum of its proper divisors (268674336).

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

82303200 is a wasteful number, since it uses less digits than its factorization.

82303200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 127 (or 111 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 18.

The square root of 82303200 is about 9072.1111104307. Note that the first 5 decimals coincide. The cubic root of 82303200 is about 434.9829561297.

Adding to 82303200 its reverse (230328), we get a palindrome (82533528).

The spelling of 82303200 in words is "eighty-two million, three hundred three thousand, two hundred".