509472 has 72 divisors (see below), whose sum is σ = 1523340. Its totient is φ = 161280.

The previous prime is 509449. The next prime is 509477. The reversal of 509472 is 274905.

It can be written as a sum of positive squares in 2 ways, for example, as 467856 + 41616 = 684^2 + 204^2 .

It is a tau number, because it is divible by the number of its divisors (72).

It is an alternating number because its digits alternate between odd and even.

It is not an unprimeable number, because it can be changed into a prime (509477) by changing a digit.

509472 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 8322 + ... + 8382.

2⁵⁰⁹⁴⁷² 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 509472, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (761670).

509472 is an abundant number, since it is smaller than the sum of its proper divisors (1013868).

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

509472 is a wasteful number, since it uses less digits than its factorization.

509472 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 106 (or 95 counting only the distinct ones).

The product of its (nonzero) digits is 2520, while the sum is 27.

The square root of 509472 is about 713.7730731822. The cubic root of 509472 is about 79.8681160356.

The spelling of 509472 in words is "five hundred nine thousand, four hundred seventy-two".