257209421414400 has 4320 divisors, whose sum is σ = 1225612149552000. Its totient is φ = 52355420651520.

The previous prime is 257209421414263. The next prime is 257209421414419. The reversal of 257209421414400 is 4414124902752.

257209421414400 is a `hidden beast` number, since 2 + 5 + 7 + 20 + 9 + 4 + 214 + 1 + 4 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (4320).

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 204296600971 + ... + 204296602229.

It is an arithmetic number, because the mean of its divisors is an integer number (283706516100).

Almost surely, 2^{257209421414400} is an apocalyptic number.

257209421414400 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 257209421414400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (612806074776000).

257209421414400 is an abundant number, since it is smaller than the sum of its proper divisors (968402728137600).

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

257209421414400 is a wasteful number, since it uses less digits than its factorization.

257209421414400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1362 (or 1318 counting only the distinct ones).

The product of its (nonzero) digits is 645120, while the sum is 45.

The spelling of 257209421414400 in words is "two hundred fifty-seven trillion, two hundred nine billion, four hundred twenty-one million, four hundred fourteen thousand, four hundred".