What are the divisors of 4522?

1, 2, 7, 14, 17, 19, 34, 38, 119, 133, 238, 266, 323, 646, 2261, 4522

There is a total of 16 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 540.

8 even divisors

2, 14, 34, 38, 238, 266, 646, 4522

8 odd divisors

1, 7, 17, 19, 119, 133, 323, 2261

How to compute the divisors of 4522?

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 4522 by each of the numbers from 1 to 4522 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)

4522 / 1 = 4522 (the remainder is 0, so 1 is a divisor of 4522)
4522 / 2 = 2261 (the remainder is 0, so 2 is a divisor of 4522)
4522 / 3 = 1507.3333333333 (the remainder is 1, so 3 is not a divisor of 4522)
...
4522 / 4521 = 1.0002211900022 (the remainder is 1, so 4521 is not a divisor of 4522)
4522 / 4522 = 1 (the remainder is 0, so 4522 is a divisor of 4522)

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 4522 (i.e. 67.245817713818). 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 $\frac{N}{d} = D$ )

4522 / 1 = 4522 (the remainder is 0, so 1 and 4522 are divisors of 4522)
4522 / 2 = 2261 (the remainder is 0, so 2 and 2261 are divisors of 4522)
4522 / 3 = 1507.3333333333 (the remainder is 1, so 3 is not a divisor of 4522)
...
4522 / 66 = 68.515151515152 (the remainder is 34, so 66 is not a divisor of 4522)
4522 / 67 = 67.492537313433 (the remainder is 33, so 67 is not a divisor of 4522)