85209600 has 240 divisors, whose sum is σ = 322711488. Its totient is φ = 19415040.

The previous prime is 85209599. The next prime is 85209643. The reversal of 85209600 is 690258.

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is an unprimeable number.

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 23 ways as a sum of consecutive naturals, for example, 268642 + ... + 268958.

Almost surely, 2^85209600 is an apocalyptic number.

85209600 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 85209600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (161355744).

85209600 is an abundant number, since it is smaller than the sum of its proper divisors (237501888).

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

85209600 is a wasteful number, since it uses less digits than its factorization.

85209600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 355 (or 334 counting only the distinct ones).

The product of its (nonzero) digits is 4320, while the sum is 30.

The square root of 85209600 is about 9230.9046143918. The cubic root of 85209600 is about 440.0440727203.

Adding to 85209600 its reverse (690258), we get a palindrome (85899858).

The spelling of 85209600 in words is "eighty-five million, two hundred nine thousand, six hundred".