What are the divisors of 4308?

1, 2, 3, 4, 6, 12, 359, 718, 1077, 1436, 2154, 4308

There is a total of 12 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 840.

8 even divisors

2, 4, 6, 12, 718, 1436, 2154, 4308

4 odd divisors

1, 3, 359, 1077

How to compute the divisors of 4308?

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 4308 by each of the numbers from 1 to 4308 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)

4308 / 1 = 4308 (the remainder is 0, so 1 is a divisor of 4308)
4308 / 2 = 2154 (the remainder is 0, so 2 is a divisor of 4308)
4308 / 3 = 1436 (the remainder is 0, so 3 is a divisor of 4308)
...
4308 / 4307 = 1.0002321801718 (the remainder is 1, so 4307 is not a divisor of 4308)
4308 / 4308 = 1 (the remainder is 0, so 4308 is a divisor of 4308)

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 4308 (i.e. 65.635356325688). 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 $\frac{N}{d} = D$ )

4308 / 1 = 4308 (the remainder is 0, so 1 and 4308 are divisors of 4308)
4308 / 2 = 2154 (the remainder is 0, so 2 and 2154 are divisors of 4308)
4308 / 3 = 1436 (the remainder is 0, so 3 and 1436 are divisors of 4308)
...
4308 / 64 = 67.3125 (the remainder is 20, so 64 is not a divisor of 4308)
4308 / 65 = 66.276923076923 (the remainder is 18, so 65 is not a divisor of 4308)