257712 has 80 divisors (see below), whose sum is σ = 833280. Its totient is φ = 66816.

The previous prime is 257711. The next prime is 257713. The reversal of 257712 is 217752.

It is an interprime number because it is at equal distance from previous prime (257711) and next prime (257713).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (257711) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 4339 + ... + 4397.

It is an arithmetic number, because the mean of its divisors is an integer number (10416).

2²⁵⁷⁷¹² 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 257712, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (416640).

257712 is an abundant number, since it is smaller than the sum of its proper divisors (575568).

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

257712 is a wasteful number, since it uses less digits than its factorization.

257712 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 90 (or 84 counting only the distinct ones).

The product of its digits is 980, while the sum is 24.

The square root of 257712 is about 507.6534250845. The cubic root of 257712 is about 63.6372709827.

It can be divided in two parts, 257 and 712, that added together give a palindrome (969).

The spelling of 257712 in words is "two hundred fifty-seven thousand, seven hundred twelve".