85384800 has 288 divisors, whose sum is σ = 318729600. Its totient is φ = 22049280.

The previous prime is 85384777. The next prime is 85384801. The reversal of 85384800 is 848358.

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (85384801) 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 47 ways as a sum of consecutive naturals, for example, 1274367 + ... + 1274433.

It is an arithmetic number, because the mean of its divisors is an integer number (1106700).

Almost surely, 2^85384800 is an apocalyptic number.

85384800 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 85384800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (159364800).

85384800 is an abundant number, since it is smaller than the sum of its proper divisors (233344800).

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

85384800 is a wasteful number, since it uses less digits than its factorization.

85384800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 155 (or 136 counting only the distinct ones).

The product of its (nonzero) digits is 30720, while the sum is 36.

The square root of 85384800 is about 9240.3896021759. The cubic root of 85384800 is about 440.3454587254.

The spelling of 85384800 in words is "eighty-five million, three hundred eighty-four thousand, eight hundred".