What are the divisors of 317?

1, 317

There is a total of 2 positive divisors.
The sum of these divisors is 318.
The arithmetic mean is 159.

2 odd divisors

1, 317

How to compute the divisors of 317?

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 317 by each of the numbers from 1 to 317 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)

317 / 1 = 317 (the remainder is 0, so 1 is a divisor of 317)
317 / 2 = 158.5 (the remainder is 1, so 2 is not a divisor of 317)
317 / 3 = 105.66666666667 (the remainder is 2, so 3 is not a divisor of 317)
...
317 / 316 = 1.003164556962 (the remainder is 1, so 316 is not a divisor of 317)
317 / 317 = 1 (the remainder is 0, so 317 is a divisor of 317)

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 317 (i.e. 17.804493814765). 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 $\frac{N}{d} = D$ )

317 / 1 = 317 (the remainder is 0, so 1 and 317 are divisors of 317)
317 / 2 = 158.5 (the remainder is 1, so 2 is not a divisor of 317)
317 / 3 = 105.66666666667 (the remainder is 2, so 3 is not a divisor of 317)
...
317 / 16 = 19.8125 (the remainder is 13, so 16 is not a divisor of 317)
317 / 17 = 18.647058823529 (the remainder is 11, so 17 is not a divisor of 317)