75628800 has 324 divisors, whose sum is σ = 294072324. Its totient is φ = 18432000.

The previous prime is 75628799. The next prime is 75628823. The reversal of 75628800 is 882657.

It can be written as a sum of positive squares in 6 ways, for example, as 147456 + 75481344 = 384^2 + 8688^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

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, 748750 + ... + 748850.

Almost surely, 2^75628800 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 75628800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (147036162).

75628800 is an abundant number, since it is smaller than the sum of its proper divisors (218443524).

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

75628800 is a wasteful number, since it uses less digits than its factorization.

75628800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 146 (or 124 counting only the distinct ones).

The product of its (nonzero) digits is 26880, while the sum is 36.

The square root of 75628800 is about 8696.4820473569. The cubic root of 75628800 is about 422.8916108117.

The spelling of 75628800 in words is "seventy-five million, six hundred twenty-eight thousand, eight hundred".