76816800 has 216 divisors, whose sum is σ = 277857216. Its totient is φ = 19960320.

The previous prime is 76816783. The next prime is 76816807. The reversal of 76816800 is 861867.

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

It is not an unprimeable number, because it can be changed into a prime (76816807) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 338287 + ... + 338513.

It is an arithmetic number, because the mean of its divisors is an integer number (1286376).

Almost surely, 2^76816800 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 76816800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (138928608).

76816800 is an abundant number, since it is smaller than the sum of its proper divisors (201040416).

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

76816800 is a wasteful number, since it uses less digits than its factorization.

76816800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 300 (or 284 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 36.

The square root of 76816800 is about 8764.5193821453. The cubic root of 76816800 is about 425.0944196216.

The spelling of 76816800 in words is "seventy-six million, eight hundred sixteen thousand, eight hundred".