101688 has 32 divisors (see below), whose sum is σ = 268800. Its totient is φ = 31968.

The previous prime is 101681. The next prime is 101693. The reversal of 101688 is 886101.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (101681) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 345 + ... + 567.

It is an arithmetic number, because the mean of its divisors is an integer number (8400).

2¹⁰¹⁶⁸⁸ 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 101688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (134400).

101688 is an abundant number, since it is smaller than the sum of its proper divisors (167112).

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

101688 is a wasteful number, since it uses less digits than its factorization.

101688 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 251 (or 247 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 24.

The square root of 101688 is about 318.8855594096. The cubic root of 101688 is about 46.6755991971.

Adding to 101688 its reverse (886101), we get a palindrome (987789).

The spelling of 101688 in words is "one hundred one thousand, six hundred eighty-eight".