763968000 has 320 divisors, whose sum is σ = 2665757952. Its totient is φ = 193740800.

The previous prime is 763967987. The next prime is 763968001. The reversal of 763968000 is 869367.

It is a tau number, because it is divible by the number of its divisors (320).

It is a self number, because there is not a number n which added to its sum of digits gives 763968000.

It is not an unprimeable number, because it can be changed into a prime (763968001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 4415914 + ... + 4416086.

Almost surely, 2^763968000 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 763968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1332878976).

763968000 is an abundant number, since it is smaller than the sum of its proper divisors (1901789952).

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

763968000 is a wasteful number, since it uses less digits than its factorization.

763968000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 232 (or 206 counting only the distinct ones).

The product of its (nonzero) digits is 54432, while the sum is 39.

The square root of 763968000 is about 27639.9710564248. The cubic root of 763968000 is about 914.1659813445.

The spelling of 763968000 in words is "seven hundred sixty-three million, nine hundred sixty-eight thousand".