507312 has 60 divisors (see below), whose sum is σ = 1534624. Its totient is φ = 155520.

The previous prime is 507301. The next prime is 507313. The reversal of 507312 is 213705.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 507312.

It is not an unprimeable number, because it can be changed into a prime (507313) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1737 + ... + 2007.

2⁵⁰⁷³¹² is an apocalyptic number.

507312 is a gapful number since it is divisible by the number (52) 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 507312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (767312).

507312 is an abundant number, since it is smaller than the sum of its proper divisors (1027312).

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

507312 is a wasteful number, since it uses less digits than its factorization.

507312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 298 (or 289 counting only the distinct ones).

The product of its (nonzero) digits is 210, while the sum is 18.

The square root of 507312 is about 712.2583800841. The cubic root of 507312 is about 79.7550843022.

The spelling of 507312 in words is "five hundred seven thousand, three hundred twelve".