257312 has 48 divisors (see below), whose sum is σ = 598752. Its totient is φ = 107520.

The previous prime is 257311. The next prime is 257321. The reversal of 257312 is 213752.

257312 is digitally balanced in base 2 and base 3, because in such bases it contains all the possibile digits an equal number of times.

It is a nialpdrome in base 8.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 257312.

It is not an unprimeable number, because it can be changed into a prime (257311) 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, 5963 + ... + 6005.

It is an arithmetic number, because the mean of its divisors is an integer number (12474).

2²⁵⁷³¹² is an apocalyptic number.

257312 is a gapful number since it is divisible by the number (22) 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 257312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (299376).

257312 is an abundant number, since it is smaller than the sum of its proper divisors (341440).

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

257312 is a wasteful number, since it uses less digits than its factorization.

257312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 81 (or 73 counting only the distinct ones).

The product of its digits is 420, while the sum is 20.

The square root of 257312 is about 507.2593025268. The cubic root of 257312 is about 63.6043297027.

It can be divided in two parts, 2573 and 12, that multiplied together give a triangular number (30876 = T₂₄₈).

The spelling of 257312 in words is "two hundred fifty-seven thousand, three hundred twelve".