75864000 has 224 divisors, whose sum is σ = 261518400. Its totient is φ = 19353600.

The previous prime is 75863999. The next prime is 75864007. The reversal of 75864000 is 46857.

It is a happy number.

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 (75864007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 695946 + ... + 696054.

Almost surely, 2^75864000 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 75864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (130759200).

75864000 is an abundant number, since it is smaller than the sum of its proper divisors (185654400).

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

75864000 is a wasteful number, since it uses less digits than its factorization.

75864000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 168 (or 148 counting only the distinct ones).

The product of its (nonzero) digits is 6720, while the sum is 30.

The square root of 75864000 is about 8709.9942594700. The cubic root of 75864000 is about 423.3295444030.

The spelling of 75864000 in words is "seventy-five million, eight hundred sixty-four thousand".