• 680 can be written using four 4's:

680 has 16 divisors (see below), whose sum is σ = 1620. Its totient is φ = 256.

The previous prime is 677. The next prime is 683. The reversal of 680 is 86.

680 = T_{1} + T_{2} + ... +
T_{15}.

It is a happy number.

680 is nontrivially palindromic in base 7 and base 13.

680 is a nontrivial binomial coefficient, being equal to C(17, 3).

It is an interprime number because it is at equal distance from previous prime (677) and next prime (683).

It can be written as a sum of positive squares in 2 ways, for example, as 676 + 4 = 26^2 + 2^2 .

680 is an undulating number in base 13.

It is a plaindrome in base 11, base 12 and base 14.

It is a nialpdrome in base 4.

It is not an unprimeable number, because it can be changed into a prime (683) by changing a digit.

It is the 15-th tetrahedral number.

In principle, a polygon with 680 sides can be constructed with ruler and compass.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 32 + ... + 48.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (810).

680 is an abundant number, since it is smaller than the sum of its proper divisors (940).

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

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

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

The sum of its prime factors is 28 (or 24 counting only the distinct ones).

The product of its (nonzero) digits is 48, while the sum is 14.

The square root of 680 is about 26.0768096208. The cubic root of 680 is about 8.7936593443.

Subtracting from 680 its sum of digits (14), we obtain a palindrome (666).

Multiplying 680 by its product of nonzero digits (48), we get a triangular number (32640 = T_{255}).

The spelling of 680 in words is "six hundred eighty", and thus it is an aban number and an oban number.

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