83688 has 32 divisors (see below), whose sum is σ = 228960. Its totient is φ = 25280.

The previous prime is 83663. The next prime is 83689. The reversal of 83688 is 88638.

It is a Harshad number since it is a multiple of its sum of digits (33).

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 83688.

It is not an unprimeable number, because it can be changed into a prime (83689) by changing a digit.

83688 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 106 + ... + 422.

It is an arithmetic number, because the mean of its divisors is an integer number (7155).

2⁸³⁶⁸⁸ is an apocalyptic number.

83688 is a gapful number since it is divisible by the number (88) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 83688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (114480).

83688 is an abundant number, since it is smaller than the sum of its proper divisors (145272).

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

83688 is a wasteful number, since it uses less digits than its factorization.

83688 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 337 (or 333 counting only the distinct ones).

The product of its digits is 9216, while the sum is 33.

The square root of 83688 is about 289.2887830525. The cubic root of 83688 is about 43.7409015093.

Subtracting 83688 from its reverse (88638), we obtain a triangular number (4950 = T₉₉).

The spelling of 83688 in words is "eighty-three thousand, six hundred eighty-eight".