1027728000 has 640 divisors, whose sum is σ = 4178013840. Its totient is φ = 248832000.

The previous prime is 1027727983. The next prime is 1027728041. The reversal of 1027728000 is 8277201.

It can be written as a sum of positive squares in 8 ways, for example, as 100160064 + 927567936 = 10008^2 + 30456^2 .

It is a tau number, because it is divible by the number of its divisors (640).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 16847970 + ... + 16848030.

Almost surely, 2^1027728000 is an apocalyptic number.

1027728000 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 1027728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2089006920).

1027728000 is an abundant number, since it is smaller than the sum of its proper divisors (3150285840).

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

1027728000 is an equidigital number, since it uses as much as digits as its factorization.

1027728000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 115 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 1568, while the sum is 27.

The square root of 1027728000 is about 32058.1970796862. The cubic root of 1027728000 is about 1009.1585318917.

The spelling of 1027728000 in words is "one billion, twenty-seven million, seven hundred twenty-eight thousand".