85632400 has 180 divisors, whose sum is σ = 254384388. Its totient is φ = 27525120.

The previous prime is 85632377. The next prime is 85632401. The reversal of 85632400 is 423658.

It can be written as a sum of positive squares in 6 ways, for example, as 9314704 + 76317696 = 3052^2 + 8736^2 .

It is a Harshad number since it is a multiple of its sum of digits (28).

It is not an unprimeable number, because it can be changed into a prime (85632401) by changing a digit.

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 35 ways as a sum of consecutive naturals, for example, 333072 + ... + 333328.

Almost surely, 2^85632400 is an apocalyptic number.

85632400 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 85632400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (127192194).

85632400 is an abundant number, since it is smaller than the sum of its proper divisors (168751988).

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

85632400 is a wasteful number, since it uses less digits than its factorization.

85632400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 306 (or 288 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 28.

The square root of 85632400 is about 9253.7776070100. Note that the first 3 decimals coincide. The cubic root of 85632400 is about 440.7706878707.

The spelling of 85632400 in words is "eighty-five million, six hundred thirty-two thousand, four hundred".