686800 has 60 divisors (see below), whose sum is σ = 1764396. Its totient is φ = 256000.

The previous prime is 686797. The next prime is 686801. The reversal of 686800 is 8686.

686800 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 6 ways, for example, as 59536 + 627264 = 244^2 + 792^2 .

It is a Smith number, since the sum of its digits (28) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (686801) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 6750 + ... + 6850.

2⁶⁸⁶⁸⁰⁰ 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 686800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (882198).

686800 is an abundant number, since it is smaller than the sum of its proper divisors (1077596).

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

686800 is a wasteful number, since it uses less digits than its factorization.

686800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 136 (or 125 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 28.

The square root of 686800 is about 828.7339742040. The cubic root of 686800 is about 88.2287437403.

It can be divided in two parts, 68 and 6800, that multiplied together give a square (462400 = 680²).

The spelling of 686800 in words is "six hundred eighty-six thousand, eight hundred".