What are the divisors of 4484?

1, 2, 4, 19, 38, 59, 76, 118, 236, 1121, 2242, 4484

There is a total of 12 positive divisors.
The sum of these divisors is 8400.
The arithmetic mean is 700.

8 even divisors

2, 4, 38, 76, 118, 236, 2242, 4484

4 odd divisors

1, 19, 59, 1121

How to compute the divisors of 4484?

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 4484 by each of the numbers from 1 to 4484 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)

4484 / 1 = 4484 (the remainder is 0, so 1 is a divisor of 4484)
4484 / 2 = 2242 (the remainder is 0, so 2 is a divisor of 4484)
4484 / 3 = 1494.6666666667 (the remainder is 2, so 3 is not a divisor of 4484)
...
4484 / 4483 = 1.0002230649119 (the remainder is 1, so 4483 is not a divisor of 4484)
4484 / 4484 = 1 (the remainder is 0, so 4484 is a divisor of 4484)

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 4484 (i.e. 66.962676171133). 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 $\frac{N}{d} = D$ )

4484 / 1 = 4484 (the remainder is 0, so 1 and 4484 are divisors of 4484)
4484 / 2 = 2242 (the remainder is 0, so 2 and 2242 are divisors of 4484)
4484 / 3 = 1494.6666666667 (the remainder is 2, so 3 is not a divisor of 4484)
...
4484 / 65 = 68.984615384615 (the remainder is 64, so 65 is not a divisor of 4484)
4484 / 66 = 67.939393939394 (the remainder is 62, so 66 is not a divisor of 4484)