448768000 has 96 divisors (see below), whose sum is σ = 1120490280. Its totient is φ = 179404800.

The previous prime is 448767971. The next prime is 448768009. The reversal of 448768000 is 867844.

It can be written as a sum of positive squares in 4 ways, for example, as 30647296 + 418120704 = 5536^2 + 20448^2 .

It is not an unprimeable number, because it can be changed into a prime (448768009) by changing a digit.

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 7 ways as a sum of consecutive naturals, for example, 255124 + ... + 256876.

Almost surely, 2^448768000 is an apocalyptic number.

448768000 is a gapful number since it is divisible by the number (40) 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 448768000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (560245140).

448768000 is an abundant number, since it is smaller than the sum of its proper divisors (671722280).

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

448768000 is an equidigital number, since it uses as much as digits as its factorization.

448768000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1790 (or 1760 counting only the distinct ones).

The product of its (nonzero) digits is 43008, while the sum is 37.

The square root of 448768000 is about 21184.1450146094. The cubic root of 448768000 is about 765.6094649076.

The spelling of 448768000 in words is "four hundred forty-eight million, seven hundred sixty-eight thousand".