What are the divisors of 4444?

1, 2, 4, 11, 22, 44, 101, 202, 404, 1111, 2222, 4444

There is a total of 12 positive divisors.
The sum of these divisors is 8568.
The arithmetic mean is 714.

8 even divisors

2, 4, 22, 44, 202, 404, 2222, 4444

4 odd divisors

1, 11, 101, 1111

How to compute the divisors of 4444?

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 4444 by each of the numbers from 1 to 4444 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)

4444 / 1 = 4444 (the remainder is 0, so 1 is a divisor of 4444)
4444 / 2 = 2222 (the remainder is 0, so 2 is a divisor of 4444)
4444 / 3 = 1481.3333333333 (the remainder is 1, so 3 is not a divisor of 4444)
...
4444 / 4443 = 1.0002250731488 (the remainder is 1, so 4443 is not a divisor of 4444)
4444 / 4444 = 1 (the remainder is 0, so 4444 is a divisor of 4444)

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 4444 (i.e. 66.663333249996). 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 $\frac{N}{d} = D$ )

4444 / 1 = 4444 (the remainder is 0, so 1 and 4444 are divisors of 4444)
4444 / 2 = 2222 (the remainder is 0, so 2 and 2222 are divisors of 4444)
4444 / 3 = 1481.3333333333 (the remainder is 1, so 3 is not a divisor of 4444)
...
4444 / 65 = 68.369230769231 (the remainder is 24, so 65 is not a divisor of 4444)
4444 / 66 = 67.333333333333 (the remainder is 22, so 66 is not a divisor of 4444)