768024000 has 168 divisors, whose sum is σ = 2747607408. Its totient is φ = 204787200.

The previous prime is 768023999. The next prime is 768024001. The reversal of 768024000 is 420867.

768024000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (768023999) and next prime (768024001).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (768024001) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 66667 + ... + 77333.

It is an arithmetic number, because the mean of its divisors is an integer number (16354806).

Almost surely, 2^768024000 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 768024000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1373803704).

768024000 is an abundant number, since it is smaller than the sum of its proper divisors (1979583408).

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

768024000 is a wasteful number, since it uses less digits than its factorization.

768024000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 10700 (or 10677 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The square root of 768024000 is about 27713.2459304211. The cubic root of 768024000 is about 915.7809332287.

Adding to 768024000 its reverse (420867), we get a palindrome (768444867).

The spelling of 768024000 in words is "seven hundred sixty-eight million, twenty-four thousand".