What are the divisors of 1308?

1, 2, 3, 4, 6, 12, 109, 218, 327, 436, 654, 1308

There is a total of 12 positive divisors.
The sum of these divisors is 3080.
The arithmetic mean is 256.66666666667.

8 even divisors

2, 4, 6, 12, 218, 436, 654, 1308

4 odd divisors

1, 3, 109, 327

How to compute the divisors of 1308?

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 1308 by each of the numbers from 1 to 1308 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)

1308 / 1 = 1308 (the remainder is 0, so 1 is a divisor of 1308)
1308 / 2 = 654 (the remainder is 0, so 2 is a divisor of 1308)
1308 / 3 = 436 (the remainder is 0, so 3 is a divisor of 1308)
...
1308 / 1307 = 1.0007651109411 (the remainder is 1, so 1307 is not a divisor of 1308)
1308 / 1308 = 1 (the remainder is 0, so 1308 is a divisor of 1308)

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 1308 (i.e. 36.16628264005). 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 $\frac{N}{d} = D$ )

1308 / 1 = 1308 (the remainder is 0, so 1 and 1308 are divisors of 1308)
1308 / 2 = 654 (the remainder is 0, so 2 and 654 are divisors of 1308)
1308 / 3 = 436 (the remainder is 0, so 3 and 436 are divisors of 1308)
...
1308 / 35 = 37.371428571429 (the remainder is 13, so 35 is not a divisor of 1308)
1308 / 36 = 36.333333333333 (the remainder is 12, so 36 is not a divisor of 1308)