83964 has 12 divisors (see below), whose sum is σ = 195944. Its totient is φ = 27984.

The previous prime is 83939. The next prime is 83969. The reversal of 83964 is 46938.

It is a tau number, because it is divible by the number of its divisors (12).

It is a d-powerful number, because it can be written as 8³ + 3⁹ + 9³ + 6⁶ + 4⁷ .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (83969) by changing a digit.

83964 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 3487 + ... + 3510.

2⁸³⁹⁶⁴ is an apocalyptic number.

It is an amenable number.

83964 is an abundant number, since it is smaller than the sum of its proper divisors (111980).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (97972).

83964 is a wasteful number, since it uses less digits than its factorization.

83964 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 7004 (or 7002 counting only the distinct ones).

The product of its digits is 5184, while the sum is 30.

The square root of 83964 is about 289.7654223678. The cubic root of 83964 is about 43.7889340490.

It can be divided in two parts, 839 and 64, that added together give a triangular number (903 = T₄₂).

The spelling of 83964 in words is "eighty-three thousand, nine hundred sixty-four".