85729200 has 120 divisors (see below), whose sum is σ = 276768000. Its totient is φ = 22682880.

The previous prime is 85729169. The next prime is 85729207. The reversal of 85729200 is 292758.

It is a tau number, because it is divible by the number of its divisors (120).

It is not an unprimeable number, because it can be changed into a prime (85729207) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 238621 + ... + 238979.

It is an arithmetic number, because the mean of its divisors is an integer number (2306400).

Almost surely, 2^85729200 is an apocalyptic number.

85729200 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 85729200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (138384000).

85729200 is an abundant number, since it is smaller than the sum of its proper divisors (191038800).

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

85729200 is a wasteful number, since it uses less digits than its factorization.

85729200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 579 (or 568 counting only the distinct ones).

The product of its (nonzero) digits is 10080, while the sum is 33.

The square root of 85729200 is about 9259.0064261777. The cubic root of 85729200 is about 440.9367096713.

The spelling of 85729200 in words is "eighty-five million, seven hundred twenty-nine thousand, two hundred".