768768000 has 768 divisors, whose sum is σ = 3434296320. Its totient is φ = 147456000.

The previous prime is 768767969. The next prime is 768768023. The reversal of 768768000 is 867867.

It is a tau number, because it is divible by the number of its divisors (768).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 59135994 + ... + 59136006.

It is an arithmetic number, because the mean of its divisors is an integer number (4471740).

Almost surely, 2^768768000 is an apocalyptic number.

768768000 is a gapful number since it is divisible by the number (70) 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 768768000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1717148160).

768768000 is an abundant number, since it is smaller than the sum of its proper divisors (2665528320).

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

768768000 is a wasteful number, since it uses less digits than its factorization.

768768000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 71 (or 41 counting only the distinct ones).

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

The square root of 768768000 is about 27726.6658651919. The cubic root of 768768000 is about 916.0765494781.

The spelling of 768768000 in words is "seven hundred sixty-eight million, seven hundred sixty-eight thousand".