768813590790144 has 945 divisors, whose sum is σ = 2359117882333849. Its totient is φ = 250425798819840.

The previous prime is 768813590789977. The next prime is 768813590790163. The reversal of 768813590790144 is 441097095318867.

The square root of 768813590790144 is 27727488.

It is a perfect power (a square), and thus also a powerful number.

768813590790144 is a `hidden beast` number, since 7 + 6 + 8 + 8 + 13 + 590 + 7 + 9 + 0 + 14 + 4 = 666.

It can be written as a sum of positive squares in only one way, i.e., 13547110809600 + 755266479980544 = 3680640^2 + 27482112^2 .

It is a super-2 number, since 2×768813590790144² (a number of 31 digits) contains 22 as substring.

It is a Smith number, since the sum of its digits (72) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is a Duffinian number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 62 ways as a sum of consecutive naturals, for example, 6803660095432 + ... + 6803660095544.

Almost surely, 2^{768813590790144} is an apocalyptic number.

768813590790144 is the 27727488-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 768813590790144

768813590790144 is an abundant number, since it is smaller than the sum of its proper divisors (1590304291543705).

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

768813590790144 is an frugal number, since it uses more digits than its factorization.

768813590790144 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 414 (or 189 counting only the distinct ones).

The product of its (nonzero) digits is 365783040, while the sum is 72.

The spelling of 768813590790144 in words is "seven hundred sixty-eight trillion, eight hundred thirteen billion, five hundred ninety million, seven hundred ninety thousand, one hundred forty-four".