257296000 has 128 divisors (see below), whose sum is σ = 689466960. Its totient is φ = 94924800.

The previous prime is 257295949. The next prime is 257296007. The reversal of 257296000 is 692752.

It can be written as a sum of positive squares in 8 ways, for example, as 3594816 + 253701184 = 1896^2 + 15928^2 .

It is a tau number, because it is divible by the number of its divisors (128).

It is not an unprimeable number, because it can be changed into a prime (257296007) 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, 207382 + ... + 208618.

Almost surely, 2^257296000 is an apocalyptic number.

257296000 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 257296000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (344733480).

257296000 is an abundant number, since it is smaller than the sum of its proper divisors (432170960).

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

257296000 is a wasteful number, since it uses less digits than its factorization.

257296000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1279 (or 1257 counting only the distinct ones).

The product of its (nonzero) digits is 7560, while the sum is 31.

The square root of 257296000 is about 16040.4488715248. The cubic root of 257296000 is about 636.0301134167.

The spelling of 257296000 in words is "two hundred fifty-seven million, two hundred ninety-six thousand".