257678064400 has 135 divisors (see below), whose sum is σ = 658070409661. Its totient is φ = 96943237120.

The previous prime is 257678064379. The next prime is 257678064403. The reversal of 257678064400 is 4460876752.

The square root of 257678064400 is 507620.

It is a perfect power (a square), and thus also a powerful number.

257678064400 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 13 ways, for example, as 11280988944 + 246397075456 = 106212^2 + 496384^2 .

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (257678064403) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 172590054 + ... + 172591546.

Almost surely, 2^257678064400 is an apocalyptic number.

257678064400 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

257678064400 is the 507620-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 257678064400

257678064400 is an abundant number, since it is smaller than the sum of its proper divisors (400392345261).

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

257678064400 is an equidigital number, since it uses as much as digits as its factorization.

257678064400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3038 (or 1517 counting only the distinct ones).

The product of its (nonzero) digits is 2257920, while the sum is 49.

Multiplying 257678064400 by its sum of digits (49), we get a square (12626225155600 = 3553340²).

The spelling of 257678064400 in words is "two hundred fifty-seven billion, six hundred seventy-eight million, sixty-four thousand, four hundred".