768001600 has 84 divisors (see below), whose sum is σ = 1940988244. Its totient is φ = 298874880.

The previous prime is 768001589. The next prime is 768001607. The reversal of 768001600 is 6100867.

It can be written as a sum of positive squares in 6 ways, for example, as 57032704 + 710968896 = 7552^2 + 26664^2 .

It is not an unprimeable number, because it can be changed into a prime (768001607) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 52714 + ... + 65686.

Almost surely, 2^768001600 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 768001600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (970494122).

768001600 is an abundant number, since it is smaller than the sum of its proper divisors (1172986644).

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

768001600 is a wasteful number, since it uses less digits than its factorization.

768001600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 13032 (or 13017 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 28.

The square root of 768001600 is about 27712.8417886005. The cubic root of 768001600 is about 915.7720299946.

It can be divided in two parts, 76800 and 1600, that added together give a square (78400 = 280²).

The spelling of 768001600 in words is "seven hundred sixty-eight million, one thousand, six hundred".