768768 has 144 divisors (see below), whose sum is σ = 2747136. Its totient is φ = 184320.

The previous prime is 768767. The next prime is 768773. The reversal of 768768 is 867867.

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

It is a nude number because it is divisible by every one of its digits.

Its product of digits (112896) is a multiple of the sum of its prime divisors (36).

It is a nialpdrome in base 16.

It is a zygodrome in base 16.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 768768.

It is not an unprimeable number, because it can be changed into a prime (768767) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 59130 + ... + 59142.

2⁷⁶⁸⁷⁶⁸ is an apocalyptic number.

768768 is a gapful number since it is divisible by the number (78) 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 768768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1373568).

768768 is an abundant number, since it is smaller than the sum of its proper divisors (1978368).

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

768768 is a wasteful number, since it uses less digits than its factorization.

768768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 50 (or 36 counting only the distinct ones).

The product of its digits is 112896, while the sum is 42.

The square root of 768768 is about 876.7941605645. The cubic root of 768768 is about 91.6076549478.

Subtracting 768768 from its reverse (867867), we obtain a palindrome (99099).

Multiplying 768768 by its reverse (867867), we get a square (667188377856 = 816816²).

The spelling of 768768 in words is "seven hundred sixty-eight thousand, seven hundred sixty-eight".