85827600 has 180 divisors, whose sum is σ = 309226736. Its totient is φ = 22861440.

The previous prime is 85827583. The next prime is 85827601. The reversal of 85827600 is 672858.

85827600 is a `hidden beast` number, since 8 + 582 + 76 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (180).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (85827601) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 96759 + ... + 97641.

Almost surely, 2^85827600 is an apocalyptic number.

85827600 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 85827600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (154613368).

85827600 is an abundant number, since it is smaller than the sum of its proper divisors (223399136).

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

85827600 is a wasteful number, since it uses less digits than its factorization.

85827600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 916 (or 893 counting only the distinct ones).

The product of its (nonzero) digits is 26880, while the sum is 36.

The square root of 85827600 is about 9264.3186473696. The cubic root of 85827600 is about 441.1053475936.

The spelling of 85827600 in words is "eighty-five million, eight hundred twenty-seven thousand, six hundred".