85200 has 60 divisors (see below), whose sum is σ = 276768. Its totient is φ = 22400.

The previous prime is 85199. The next prime is 85201. The reversal of 85200 is 258.

85200 = T₉ + T₁₀ + ... + T₇₉.

It is an interprime number because it is at equal distance from previous prime (85199) and next prime (85201).

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a nialpdrome in base 10.

It is a self number, because there is not a number n which added to its sum of digits gives 85200.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (85201) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1165 + ... + 1235.

2⁸⁵²⁰⁰ is an apocalyptic number.

85200 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 85200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (138384).

85200 is an abundant number, since it is smaller than the sum of its proper divisors (191568).

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

85200 is a wasteful number, since it uses less digits than its factorization.

85200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 92 (or 81 counting only the distinct ones).

The product of its (nonzero) digits is 80, while the sum is 15.

The square root of 85200 is about 291.8903903865. The cubic root of 85200 is about 44.0027546485.

Adding to 85200 its reverse (258), we get a palindrome (85458).

The spelling of 85200 in words is "eighty-five thousand, two hundred".