75878400 has 312 divisors, whose sum is σ = 284391520. Its totient is φ = 17694720.

The previous prime is 75878389. The next prime is 75878401. The reversal of 75878400 is 487857.

It is a tau number, because it is divible by the number of its divisors (312).

It is a super-4 number, since 4×75878400⁴ (a number of 33 digits) contains 4444 as substring.

It is a Harshad number since it is a multiple of its sum of digits (39).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (75878401) 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 23 ways as a sum of consecutive naturals, for example, 3993591 + ... + 3993609.

Almost surely, 2^75878400 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 75878400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (142195760).

75878400 is an abundant number, since it is smaller than the sum of its proper divisors (208513120).

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

75878400 is a wasteful number, since it uses less digits than its factorization.

75878400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 69 (or 42 counting only the distinct ones).

The product of its (nonzero) digits is 62720, while the sum is 39.

The square root of 75878400 is about 8710.8208568424. The cubic root of 75878400 is about 423.3563272415.

It can be divided in two parts, 75 and 878400, that added together give a triangular number (878475 = T₁₃₂₅).

The spelling of 75878400 in words is "seventy-five million, eight hundred seventy-eight thousand, four hundred".