83200 has 54 divisors (see below), whose sum is σ = 221774. Its totient is φ = 30720.

The previous prime is 83177. The next prime is 83203. The reversal of 83200 is 238.

It can be written as a sum of positive squares in 3 ways, for example, as 256 + 82944 = 16^2 + 288^2 .

It is a Harshad number since it is a multiple of its sum of digits (13).

It is a plaindrome in base 14.

It is a nialpdrome in base 10.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (83203) by changing a digit.

83200 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 6394 + ... + 6406.

2⁸³²⁰⁰ is an apocalyptic number.

83200 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 83200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (110887).

83200 is an abundant number, since it is smaller than the sum of its proper divisors (138574).

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

83200 is a wasteful number, since it uses less digits than its factorization.

83200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 39 (or 20 counting only the distinct ones).

The product of its (nonzero) digits is 48, while the sum is 13.

The square root of 83200 is about 288.4441020371. Note that the first 3 decimals coincide. The cubic root of 83200 is about 43.6557153224.

Multiplying 83200 by its sum of digits (13), we get a square (1081600 = 1040²).

83200 divided by its sum of digits (13) gives a square (6400 = 80²).

Adding to 83200 its reverse (238), we get a palindrome (83438).

It can be divided in two parts, 8 and 3200, that multiplied together give a square (25600 = 160²).

The spelling of 83200 in words is "eighty-three thousand, two hundred".