509952 has 48 divisors (see below), whose sum is σ = 1375920. Its totient is φ = 167936.

The previous prime is 509947. The next prime is 509959. The reversal of 509952 is 259905.

It is a tau number, because it is divible by the number of its divisors (48).

It is not an unprimeable number, because it can be changed into a prime (509959) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 6103 + ... + 6185.

It is an arithmetic number, because the mean of its divisors is an integer number (28665).

2⁵⁰⁹⁹⁵² 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 509952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (687960).

509952 is an abundant number, since it is smaller than the sum of its proper divisors (865968).

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

509952 is an equidigital number, since it uses as much as digits as its factorization.

509952 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 108 (or 88 counting only the distinct ones).

The product of its (nonzero) digits is 4050, while the sum is 30.

The square root of 509952 is about 714.1092353415. The cubic root of 509952 is about 79.8931907942.

Subtracting from 509952 its reverse (259905), we obtain a cube (250047 = 63³).

It can be divided in two parts, 5099 and 52, that added together give a triangular number (5151 = T₁₀₁).

The spelling of 509952 in words is "five hundred nine thousand, nine hundred fifty-two".