1057728000 has 320 divisors, whose sum is σ = 4024171008. Its totient is φ = 241459200.

The previous prime is 1057727989. The next prime is 1057728037. The reversal of 1057728000 is 8277501.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (320).

It is a super-2 number, since 2×1057728000² = 2237577043968000000, which contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 1343607 + ... + 1344393.

Almost surely, 2^1057728000 is an apocalyptic number.

1057728000 is a gapful number since it is divisible by the number (10) 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 1057728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2012085504).

1057728000 is an abundant number, since it is smaller than the sum of its proper divisors (2966443008).

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

1057728000 is an frugal number, since it uses more digits than its factorization.

1057728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 830 (or 804 counting only the distinct ones).

The product of its (nonzero) digits is 3920, while the sum is 30.

The square root of 1057728000 is about 32522.7305126737. The cubic root of 1057728000 is about 1018.8838232372.

The spelling of 1057728000 in words is "one billion, fifty-seven million, seven hundred twenty-eight thousand".