75806400 has 168 divisors, whose sum is σ = 263621520. Its totient is φ = 19005440.

The previous prime is 75806369. The next prime is 75806431. The reversal of 75806400 is 460857.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (75806369) and next prime (75806431).

It is a super-2 number, since 2×75806400² = 11493220561920000, which contains 22 as substring.

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

It is a zygodrome in base 8.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 81136 + ... + 82064.

Almost surely, 2^75806400 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 75806400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131810760).

75806400 is an abundant number, since it is smaller than the sum of its proper divisors (187815120).

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

75806400 is a wasteful number, since it uses less digits than its factorization.

75806400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 971 (or 956 counting only the distinct ones).

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

The square root of 75806400 is about 8706.6870852236. The cubic root of 75806400 is about 423.2223791444. Note that the first 3 decimals are identical.

The spelling of 75806400 in words is "seventy-five million, eight hundred six thousand, four hundred".