75385200 has 120 divisors (see below), whose sum is σ = 263483136. Its totient is φ = 18272000.

The previous prime is 75385187. The next prime is 75385201. The reversal of 75385200 is 258357.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (75385201) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 10345 + ... + 16055.

Almost surely, 2^75385200 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 75385200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131741568).

75385200 is an abundant number, since it is smaller than the sum of its proper divisors (188097936).

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

75385200 is a wasteful number, since it uses less digits than its factorization.

75385200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5743 (or 5732 counting only the distinct ones).

The product of its (nonzero) digits is 8400, while the sum is 30.

The square root of 75385200 is about 8682.4650877501. The cubic root of 75385200 is about 422.4370785002.

The spelling of 75385200 in words is "seventy-five million, three hundred eighty-five thousand, two hundred".