509352 has 32 divisors (see below), whose sum is σ = 1341600. Its totient is φ = 160704.

The previous prime is 509329. The next prime is 509359. The reversal of 509352 is 253905.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a d-powerful number, because it can be written as 5⁴ + 0 + 3¹⁰ + 9⁵ + 5⁸ + 2² .

It is a plaindrome in base 13.

It is not an unprimeable number, because it can be changed into a prime (509359) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 103 + ... + 1014.

It is an arithmetic number, because the mean of its divisors is an integer number (41925).

2⁵⁰⁹³⁵² 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 509352, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (670800).

509352 is an abundant number, since it is smaller than the sum of its proper divisors (832248).

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

509352 is a wasteful number, since it uses less digits than its factorization.

509352 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1145 (or 1141 counting only the distinct ones).

The product of its (nonzero) digits is 1350, while the sum is 24.

The square root of 509352 is about 713.6890079019. The cubic root of 509352 is about 79.8618448852.

It can be divided in two parts, 509 and 352, that added together give a triangular number (861 = T₄₁).

The spelling of 509352 in words is "five hundred nine thousand, three hundred fifty-two".