766096800 has 288 divisors, whose sum is σ = 2943811584. Its totient is φ = 169344000.

The previous prime is 766096787. The next prime is 766096801. The reversal of 766096800 is 8690667.

It is a happy number.

766096800 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (42).

It is not an unprimeable number, because it can be changed into a prime (766096801) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 520065 + ... + 521535.

It is an arithmetic number, because the mean of its divisors is an integer number (10221568).

Almost surely, 2^766096800 is an apocalyptic number.

766096800 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 766096800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1471905792).

766096800 is an abundant number, since it is smaller than the sum of its proper divisors (2177714784).

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

766096800 is a wasteful number, since it uses less digits than its factorization.

766096800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1532 (or 1519 counting only the distinct ones).

The product of its (nonzero) digits is 108864, while the sum is 42.

The square root of 766096800 is about 27678.4537140354. The cubic root of 766096800 is about 915.0143029805.

The spelling of 766096800 in words is "seven hundred sixty-six million, ninety-six thousand, eight hundred".