What are the divisors of 4520?

1, 2, 4, 5, 8, 10, 20, 40, 113, 226, 452, 565, 904, 1130, 2260, 4520

There is a total of 16 positive divisors.
The sum of these divisors is 10260.
The arithmetic mean is 641.25.

12 even divisors

2, 4, 8, 10, 20, 40, 226, 452, 904, 1130, 2260, 4520

4 odd divisors

1, 5, 113, 565

How to compute the divisors of 4520?

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 4520 by each of the numbers from 1 to 4520 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)

4520 / 1 = 4520 (the remainder is 0, so 1 is a divisor of 4520)
4520 / 2 = 2260 (the remainder is 0, so 2 is a divisor of 4520)
4520 / 3 = 1506.6666666667 (the remainder is 2, so 3 is not a divisor of 4520)
...
4520 / 4519 = 1.0002212878956 (the remainder is 1, so 4519 is not a divisor of 4520)
4520 / 4520 = 1 (the remainder is 0, so 4520 is a divisor of 4520)

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 4520 (i.e. 67.230945255886). 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 $\frac{N}{d} = D$ )

4520 / 1 = 4520 (the remainder is 0, so 1 and 4520 are divisors of 4520)
4520 / 2 = 2260 (the remainder is 0, so 2 and 2260 are divisors of 4520)
4520 / 3 = 1506.6666666667 (the remainder is 2, so 3 is not a divisor of 4520)
...
4520 / 66 = 68.484848484848 (the remainder is 32, so 66 is not a divisor of 4520)
4520 / 67 = 67.462686567164 (the remainder is 31, so 67 is not a divisor of 4520)