257664000 has 352 divisors, whose sum is σ = 950332032. Its totient is φ = 61440000.

The previous prime is 257663969. The next prime is 257664007. The reversal of 257664000 is 466752.

It is a tau number, because it is divible by the number of its divisors (352).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is not an unprimeable number, because it can be changed into a prime (257664007) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 4223970 + ... + 4224030.

Almost surely, 2^257664000 is an apocalyptic number.

257664000 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 257664000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (475166016).

257664000 is an abundant number, since it is smaller than the sum of its proper divisors (692668032).

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

257664000 is a wasteful number, since it uses less digits than its factorization.

257664000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 110 (or 82 counting only the distinct ones).

The product of its (nonzero) digits is 10080, while the sum is 30.

The square root of 257664000 is about 16051.9157735144. The cubic root of 257664000 is about 636.3331982968. Note that the first 3 decimals are identical.

The spelling of 257664000 in words is "two hundred fifty-seven million, six hundred sixty-four thousand".