• 688 can be written using four 4's:

688 has 10 divisors (see below), whose sum is σ = 1364. Its totient is φ = 336.

The previous prime is 683. The next prime is 691. The reversal of 688 is 886.

688 is nontrivially palindromic in base 7 and base 12.

It is an Ulam number.

688 is an undulating number in base 12.

It is a plaindrome in base 10.

It is a nialpdrome in base 3 and base 9.

It is a zygodrome in base 3.

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

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 6 + ... + 37.

688 is a Friedman number, since it can be written as 86*8, using all its digits and the basic arithmetic operations.

It is an amenable number.

688 is a deficient number, since it is larger than the sum of its proper divisors (676).

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

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

The sum of its prime factors is 51 (or 45 counting only the distinct ones).

The product of its digits is 384, while the sum is 22.

The square root of 688 is about 26.2297540972. The cubic root of 688 is about 8.8280099249.

Subtracting from 688 its sum of digits (22), we obtain a palindrome (666).

It can be divided in two parts, 6 and 88, that multiplied together give a triangular number (528 = T_{32}).

The spelling of 688 in words is "six hundred eighty-eight", and thus it is an aban number and an oban number.

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