448800 has 144 divisors (see below), whose sum is σ = 1687392. Its totient is φ = 102400.

The previous prime is 448793. The next prime is 448801. The reversal of 448800 is 8844.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a zygodrome in base 10.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 448800.

It is not an unprimeable number, because it can be changed into a prime (448801) by changing a digit.

448800 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 26392 + ... + 26408.

It is an arithmetic number, because the mean of its divisors is an integer number (11718).

2⁴⁴⁸⁸⁰⁰ is an apocalyptic number.

448800 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 448800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (843696).

448800 is an abundant number, since it is smaller than the sum of its proper divisors (1238592).

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

448800 is a wasteful number, since it uses less digits than its factorization.

448800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 51 (or 38 counting only the distinct ones).

The product of its (nonzero) digits is 1024, while the sum is 24.

The square root of 448800 is about 669.9253689778. The cubic root of 448800 is about 76.5627662076.

The spelling of 448800 in words is "four hundred forty-eight thousand, eight hundred".