1261728000 has 432 divisors, whose sum is σ = 4903809456. Its totient is φ = 309657600.

The previous prime is 1261727989. The next prime is 1261728011. The reversal of 1261728000 is 8271621.

It is an interprime number because it is at equal distance from previous prime (1261727989) and next prime (1261728011).

It can be written as a sum of positive squares in 8 ways, for example, as 799305984 + 462422016 = 28272^2 + 21504^2 .

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3743832 + ... + 3744168.

Almost surely, 2^1261728000 is an apocalyptic number.

1261728000 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 1261728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2451904728).

1261728000 is an abundant number, since it is smaller than the sum of its proper divisors (3642081456).

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

1261728000 is a wasteful number, since it uses less digits than its factorization.

1261728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 387 (or 360 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 27.

The square root of 1261728000 is about 35520.8108015569. The cubic root of 1261728000 is about 1080.5758246197.

Adding to 1261728000 its reverse (8271621), we get a palindrome (1269999621).

The spelling of 1261728000 in words is "one billion, two hundred sixty-one million, seven hundred twenty-eight thousand".