677768 has 64 divisors (see below), whose sum is σ = 1680000. Its totient is φ = 254016.

The previous prime is 677767. The next prime is 677779. The reversal of 677768 is 867776.

It is a Smith number, since the sum of its digits (41) coincides with the sum of the digits of its prime factors.

It is a nialpdrome in base 7.

It is a zygodrome in base 7.

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 677768.

It is not an unprimeable number, because it can be changed into a prime (677767) 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, 35663 + ... + 35681.

It is an arithmetic number, because the mean of its divisors is an integer number (26250).

2⁶⁷⁷⁷⁶⁸ 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 677768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (840000).

677768 is an abundant number, since it is smaller than the sum of its proper divisors (1002232).

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

677768 is a wasteful number, since it uses less digits than its factorization.

677768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 59 (or 41 counting only the distinct ones).

The product of its digits is 98784, while the sum is 41.

The square root of 677768 is about 823.2666639674. The cubic root of 677768 is about 87.8402750038.

The spelling of 677768 in words is "six hundred seventy-seven thousand, seven hundred sixty-eight".