727668800 has 84 divisors (see below), whose sum is σ = 1824516036. Its totient is φ = 285542400.

The previous prime is 727668793. The next prime is 727668827. The reversal of 727668800 is 8866727.

It is a happy number.

It can be written as a sum of positive squares in 6 ways, for example, as 116985856 + 610682944 = 10816^2 + 24712^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 80510 + ... + 89090.

It is an arithmetic number, because the mean of its divisors is an integer number (21720429).

Almost surely, 2^727668800 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 727668800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (912258018).

727668800 is an abundant number, since it is smaller than the sum of its proper divisors (1096847236).

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

727668800 is a wasteful number, since it uses less digits than its factorization.

727668800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 8656 (or 8641 counting only the distinct ones).

The product of its (nonzero) digits is 225792, while the sum is 44.

The square root of 727668800 is about 26975.3368839019. The cubic root of 727668800 is about 899.4518472806.

The spelling of 727668800 in words is "seven hundred twenty-seven million, six hundred sixty-eight thousand, eight hundred".