5385600 has 288 divisors, whose sum is σ = 22197240. Its totient is φ = 1228800.

The previous prime is 5385593. The next prime is 5385613. The reversal of 5385600 is 65835.

5385600 is a `hidden beast` number, since 53 + 8 + 5 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a congruent number.

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, 316792 + ... + 316808.

Almost surely, 2^5385600 is an apocalyptic number.

5385600 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 5385600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (11098620).

5385600 is an abundant number, since it is smaller than the sum of its proper divisors (16811640).

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

5385600 is a wasteful number, since it uses less digits than its factorization.

5385600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 58 (or 38 counting only the distinct ones).

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

The square root of 5385600 is about 2320.6895526976. The cubic root of 5385600 is about 175.2849778542.

The spelling of 5385600 in words is "five million, three hundred eighty-five thousand, six hundred".