53085600 has 216 divisors, whose sum is σ = 191636172. Its totient is φ = 13824000.

The previous prime is 53085581. The next prime is 53085623. The reversal of 53085600 is 658035.

53085600 is a `hidden beast` number, since 53 + 0 + 8 + 5 + 600 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 36144144 + 16941456 = 6012^2 + 4116^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 525550 + ... + 525650.

Almost surely, 2^53085600 is an apocalyptic number.

53085600 is a gapful number since it is divisible by the number (50) 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 53085600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (95818086).

53085600 is an abundant number, since it is smaller than the sum of its proper divisors (138550572).

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

53085600 is a wasteful number, since it uses less digits than its factorization.

53085600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 200 (or 184 counting only the distinct ones).

The product of its (nonzero) digits is 3600, while the sum is 27.

The square root of 53085600 is about 7285.9865495347. The cubic root of 53085600 is about 375.8306918441.

The spelling of 53085600 in words is "fifty-three million, eighty-five thousand, six hundred".