257984000 has 160 divisors (see below), whose sum is σ = 670269600. Its totient is φ = 98918400.

The previous prime is 257983991. The next prime is 257984021. The reversal of 257984000 is 489752.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (160).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1855931 + ... + 1856069.

It is an arithmetic number, because the mean of its divisors is an integer number (4189185).

Almost surely, 2^257984000 is an apocalyptic number.

257984000 is a gapful number since it is divisible by the number (20) 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 257984000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (335134800).

257984000 is an abundant number, since it is smaller than the sum of its proper divisors (412285600).

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

257984000 is an equidigital number, since it uses as much as digits as its factorization.

257984000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 201 (or 175 counting only the distinct ones).

The product of its (nonzero) digits is 20160, while the sum is 35.

The square root of 257984000 is about 16061.8803382418. The cubic root of 257984000 is about 636.5965158797.

The spelling of 257984000 in words is "two hundred fifty-seven million, nine hundred eighty-four thousand".