85344000 has 288 divisors, whose sum is σ = 326516736. Its totient is φ = 19353600.

The previous prime is 85343989. The next prime is 85344043. The reversal of 85344000 is 44358.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 671937 + ... + 672063.

Almost surely, 2^85344000 is an apocalyptic number.

85344000 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

85344000 is the 5334-th octagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 85344000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (163258368).

85344000 is an abundant number, since it is smaller than the sum of its proper divisors (241172736).

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

85344000 is a wasteful number, since it uses less digits than its factorization.

85344000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 168 (or 144 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 24.

The square root of 85344000 is about 9238.1816392621. The cubic root of 85344000 is about 440.2753097953.

Adding to 85344000 its reverse (44358), we get a palindrome (85388358).

The spelling of 85344000 in words is "eighty-five million, three hundred forty-four thousand".