257968800 has 216 divisors, whose sum is σ = 944064576. Its totient is φ = 68739840.

The previous prime is 257968793. The next prime is 257968807. The reversal of 257968800 is 8869752.

It is an interprime number because it is at equal distance from previous prime (257968793) and next prime (257968807).

It is a tau number, because it is divible by the number of its divisors (216).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (257968807) 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 35 ways as a sum of consecutive naturals, for example, 193737 + ... + 195063.

Almost surely, 2^257968800 is an apocalyptic number.

257968800 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 257968800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (472032288).

257968800 is an abundant number, since it is smaller than the sum of its proper divisors (686095776).

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

257968800 is a wasteful number, since it uses less digits than its factorization.

257968800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1362 (or 1337 counting only the distinct ones).

The product of its (nonzero) digits is 241920, while the sum is 45.

The square root of 257968800 is about 16061.4071612670. The cubic root of 257968800 is about 636.5840132218.

It can be divided in two parts, 25796 and 8800, that added together give a square (34596 = 186²).

The spelling of 257968800 in words is "two hundred fifty-seven million, nine hundred sixty-eight thousand, eight hundred".