29664 has 36 divisors (see below), whose sum is σ = 85176. Its totient is φ = 9792.

The previous prime is 29663. The next prime is 29669. The reversal of 29664 is 46692.

It is a tau number, because it is divible by the number of its divisors (36).

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

Its product of digits (2592) is a multiple of the sum of its prime divisors (108).

It is a zygodrome in base 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (29663) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 237 + ... + 339.

It is an arithmetic number, because the mean of its divisors is an integer number (2366).

2²⁹⁶⁶⁴ is an apocalyptic number.

29664 is a gapful number since it is divisible by the number (24) 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 29664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (42588).

29664 is an abundant number, since it is smaller than the sum of its proper divisors (55512).

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

29664 is a wasteful number, since it uses less digits than its factorization.

29664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 119 (or 108 counting only the distinct ones).

The product of its digits is 2592, while the sum is 27.

The square root of 29664 is about 172.2324011329. The cubic root of 29664 is about 30.9558859185.

Subtracting from 29664 its product of digits (2592), we obtain a palindrome (27072).

The spelling of 29664 in words is "twenty-nine thousand, six hundred sixty-four".