85824000 has 240 divisors, whose sum is σ = 311196600. Its totient is φ = 22732800.

The previous prime is 85823993. The next prime is 85824023. The reversal of 85824000 is 42858.

It can be written as a sum of positive squares in 4 ways, for example, as 10342656 + 75481344 = 3216^2 + 8688^2 .

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

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 575926 + ... + 576074.

Almost surely, 2^85824000 is an apocalyptic number.

85824000 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 85824000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (155598300).

85824000 is an abundant number, since it is smaller than the sum of its proper divisors (225372600).

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

85824000 is a wasteful number, since it uses less digits than its factorization.

85824000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 188 (or 159 counting only the distinct ones).

The product of its (nonzero) digits is 2560, while the sum is 27.

The square root of 85824000 is about 9264.1243514970. The cubic root of 85824000 is about 441.0991801857.

Adding to 85824000 its reverse (42858), we get a palindrome (85866858).

The spelling of 85824000 in words is "eighty-five million, eight hundred twenty-four thousand".