What are the divisors of 4580?

1, 2, 4, 5, 10, 20, 229, 458, 916, 1145, 2290, 4580

There is a total of 12 positive divisors.
The sum of these divisors is 9660.
The arithmetic mean is 805.

8 even divisors

2, 4, 10, 20, 458, 916, 2290, 4580

4 odd divisors

1, 5, 229, 1145

How to compute the divisors of 4580?

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 4580 by each of the numbers from 1 to 4580 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)

4580 / 1 = 4580 (the remainder is 0, so 1 is a divisor of 4580)
4580 / 2 = 2290 (the remainder is 0, so 2 is a divisor of 4580)
4580 / 3 = 1526.6666666667 (the remainder is 2, so 3 is not a divisor of 4580)
...
4580 / 4579 = 1.0002183882944 (the remainder is 1, so 4579 is not a divisor of 4580)
4580 / 4580 = 1 (the remainder is 0, so 4580 is a divisor of 4580)

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 4580 (i.e. 67.675697262755). 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 $\frac{N}{d} = D$ )

4580 / 1 = 4580 (the remainder is 0, so 1 and 4580 are divisors of 4580)
4580 / 2 = 2290 (the remainder is 0, so 2 and 2290 are divisors of 4580)
4580 / 3 = 1526.6666666667 (the remainder is 2, so 3 is not a divisor of 4580)
...
4580 / 66 = 69.393939393939 (the remainder is 26, so 66 is not a divisor of 4580)
4580 / 67 = 68.358208955224 (the remainder is 24, so 67 is not a divisor of 4580)