75638400 has 96 divisors (see below), whose sum is σ = 249165600. Its totient is φ = 20167680.

The previous prime is 75638393. The next prime is 75638401. The reversal of 75638400 is 483657.

It is a tau number, because it is divible by the number of its divisors (96).

It is not an unprimeable number, because it can be changed into a prime (75638401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 5661 + ... + 13539.

It is an arithmetic number, because the mean of its divisors is an integer number (2595475).

Almost surely, 2^75638400 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 75638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (124582800).

75638400 is an abundant number, since it is smaller than the sum of its proper divisors (173527200).

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

75638400 is a wasteful number, since it uses less digits than its factorization.

75638400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 7906 (or 7889 counting only the distinct ones).

The product of its (nonzero) digits is 20160, while the sum is 33.

The square root of 75638400 is about 8697.0339771672. The cubic root of 75638400 is about 422.9095034121.

The spelling of 75638400 in words is "seventy-five million, six hundred thirty-eight thousand, four hundred".