What are the divisors of 1317?

1, 3, 439, 1317

There is a total of 4 positive divisors.
The sum of these divisors is 1760.
The arithmetic mean is 440.

4 odd divisors

1, 3, 439, 1317

How to compute the divisors of 1317?

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 1317 by each of the numbers from 1 to 1317 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)

1317 / 1 = 1317 (the remainder is 0, so 1 is a divisor of 1317)
1317 / 2 = 658.5 (the remainder is 1, so 2 is not a divisor of 1317)
1317 / 3 = 439 (the remainder is 0, so 3 is a divisor of 1317)
...
1317 / 1316 = 1.0007598784195 (the remainder is 1, so 1316 is not a divisor of 1317)
1317 / 1317 = 1 (the remainder is 0, so 1317 is a divisor of 1317)

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 1317 (i.e. 36.290494623248). 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 $\frac{N}{d} = D$ )

1317 / 1 = 1317 (the remainder is 0, so 1 and 1317 are divisors of 1317)
1317 / 2 = 658.5 (the remainder is 1, so 2 is not a divisor of 1317)
1317 / 3 = 439 (the remainder is 0, so 3 and 439 are divisors of 1317)
...
1317 / 35 = 37.628571428571 (the remainder is 22, so 35 is not a divisor of 1317)
1317 / 36 = 36.583333333333 (the remainder is 21, so 36 is not a divisor of 1317)