What are the divisors of 4448?

1, 2, 4, 8, 16, 32, 139, 278, 556, 1112, 2224, 4448

There is a total of 12 positive divisors.
The sum of these divisors is 8820.
The arithmetic mean is 735.

10 even divisors

2, 4, 8, 16, 32, 278, 556, 1112, 2224, 4448

2 odd divisors

1, 139

How to compute the divisors of 4448?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 4448 by each of the numbers from 1 to 4448 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

4448 / 1 = 4448 (the remainder is 0, so 1 is a divisor of 4448)
4448 / 2 = 2224 (the remainder is 0, so 2 is a divisor of 4448)
4448 / 3 = 1482.6666666667 (the remainder is 2, so 3 is not a divisor of 4448)
...
4448 / 4447 = 1.0002248706993 (the remainder is 1, so 4447 is not a divisor of 4448)
4448 / 4448 = 1 (the remainder is 0, so 4448 is a divisor of 4448)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 4448 (i.e. 66.693328002132). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

4448 / 1 = 4448 (the remainder is 0, so 1 and 4448 are divisors of 4448)
4448 / 2 = 2224 (the remainder is 0, so 2 and 2224 are divisors of 4448)
4448 / 3 = 1482.6666666667 (the remainder is 2, so 3 is not a divisor of 4448)
...
4448 / 65 = 68.430769230769 (the remainder is 28, so 65 is not a divisor of 4448)
4448 / 66 = 67.393939393939 (the remainder is 26, so 66 is not a divisor of 4448)