85644000 has 384 divisors, whose sum is σ = 341228160. Its totient is φ = 20736000.

The previous prime is 85643993. The next prime is 85644017. The reversal of 85644000 is 44658.

85644000 = 141³ + 142³ + ... + 164³.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a zygodrome in base 15.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 1403970 + ... + 1404030.

It is an arithmetic number, because the mean of its divisors is an integer number (888615).

Almost surely, 2^85644000 is an apocalyptic number.

85644000 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 85644000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (170614080).

85644000 is an abundant number, since it is smaller than the sum of its proper divisors (255584160).

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

85644000 is a wasteful number, since it uses less digits than its factorization.

85644000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 108 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The square root of 85644000 is about 9254.4043568454. The cubic root of 85644000 is about 440.7905896413.

Adding to 85644000 its reverse (44658), we get a palindrome (85688658).

The spelling of 85644000 in words is "eighty-five million, six hundred forty-four thousand".