83664 has 60 divisors (see below), whose sum is σ = 270816. Its totient is φ = 23616.

The previous prime is 83663. The next prime is 83689. The reversal of 83664 is 46638.

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 83664.

It is not an unprimeable number, because it can be changed into a prime (83663) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 967 + ... + 1049.

2⁸³⁶⁶⁴ is an apocalyptic number.

83664 is a gapful number since it is divisible by the number (84) 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 83664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (135408).

83664 is an abundant number, since it is smaller than the sum of its proper divisors (187152).

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

83664 is a wasteful number, since it uses less digits than its factorization.

83664 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 104 (or 95 counting only the distinct ones).

The product of its digits is 3456, while the sum is 27.

The square root of 83664 is about 289.2472990367. The cubic root of 83664 is about 43.7367197787.

Subtracting from 83664 its product of digits (3456), we obtain a palindrome (80208).

It can be divided in two parts, 836 and 64, that added together give a square (900 = 30²).

The spelling of 83664 in words is "eighty-three thousand, six hundred sixty-four".