448128 has 48 divisors (see below), whose sum is σ = 1292850. Its totient is φ = 148992.

The previous prime is 448121. The next prime is 448139. The reversal of 448128 is 821844.

448128 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in only one way, i.e., 419904 + 28224 = 648^2 + 168^2 .

It is a tau number, because it is divible by the number of its divisors (48).

It is a nude number because it is divisible by every one of its digits.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 448128.

It is not an unprimeable number, because it can be changed into a prime (448121) by changing a digit.

448128 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 5 ways as a sum of consecutive naturals, for example, 958 + ... + 1346.

2⁴⁴⁸¹²⁸ is an apocalyptic number.

448128 is a gapful number since it is divisible by the number (48) 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 448128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (646425).

448128 is an abundant number, since it is smaller than the sum of its proper divisors (844722).

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

448128 is a wasteful number, since it uses less digits than its factorization.

448128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 409 (or 394 counting only the distinct ones).

The product of its digits is 2048, while the sum is 27.

The square root of 448128 is about 669.4236326871. The cubic root of 448128 is about 76.5245339739.

It can be divided in two parts, 448 and 128, that added together give a square (576 = 24²).

The spelling of 448128 in words is "four hundred forty-eight thousand, one hundred twenty-eight".