766800 has 120 divisors (see below), whose sum is σ = 2767680. Its totient is φ = 201600.

The previous prime is 766793. The next prime is 766807. The reversal of 766800 is 8667.

766800 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 (766793) and next prime (766807).

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (766807) 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, 10765 + ... + 10835.

It is an arithmetic number, because the mean of its divisors is an integer number (23064).

2⁷⁶⁶⁸⁰⁰ 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 766800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1383840).

766800 is an abundant number, since it is smaller than the sum of its proper divisors (2000880).

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

766800 is a wasteful number, since it uses less digits than its factorization.

766800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 98 (or 81 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 27.

The square root of 766800 is about 875.6711711596. The cubic root of 766800 is about 91.5294181140.

The spelling of 766800 in words is "seven hundred sixty-six thousand, eight hundred".