1688 has 8 divisors (see below), whose sum is σ = 3180. Its totient is φ = 840.

The previous prime is 1669. The next prime is 1693. The reversal of 1688 is 8861.

1688 is nontrivially palindromic in base 14.

It is a tau number, because it is divible by the number of its divisors (8).

1688 is a modest number, since divided by 88 gives 16 as remainder.

1688 is a nontrivial repdigit in base 14.

It is a plaindrome in base 10, base 14 and base 15.

It is a nialpdrome in base 12 and base 14.

It is a zygodrome in base 14.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 98 + ... + 113.

2¹⁶⁸⁸ is an apocalyptic number.

It is an amenable number.

1688 is a deficient number, since it is larger than the sum of its proper divisors (1492).

1688 is a wasteful number, since it uses less digits than its factorization.

1688 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 217 (or 213 counting only the distinct ones).

The product of its digits is 384, while the sum is 23.

The square root of 1688 is about 41.0852771683. The cubic root of 1688 is about 11.9066836263.

Adding to 1688 its sum of digits (23), we get a triangular number (1711 = T₅₈).

The spelling of 1688 in words is "one thousand, six hundred eighty-eight".