29952 has 54 divisors (see below), whose sum is σ = 93002. Its totient is φ = 9216.

The previous prime is 29947. The next prime is 29959. The reversal of 29952 is 25992.

29952 = 18³ + 19³ + ... + 21³.

It can be written as a sum of positive squares in only one way, i.e., 20736 + 9216 = 144^2 + 96^2 .

Its product of digits (1620) is a multiple of the sum of its prime divisors (18).

It is a nialpdrome in base 16.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (29959) by changing a digit.

29952 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 (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 2298 + ... + 2310.

2²⁹⁹⁵² 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 29952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (46501).

29952 is an abundant number, since it is smaller than the sum of its proper divisors (63050).

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

29952 is a wasteful number, since it uses less digits than its factorization.

29952 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 35 (or 18 counting only the distinct ones).

The product of its digits is 1620, while the sum is 27.

The square root of 29952 is about 173.0664612223. The cubic root of 29952 is about 31.0557443066.

It can be divided in two parts, 299 and 52, that added together give a triangular number (351 = T₂₆).

The spelling of 29952 in words is "twenty-nine thousand, nine hundred fifty-two".