What are the divisors of 4317?

1, 3, 1439, 4317

There is a total of 4 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 1440.

4 odd divisors

1, 3, 1439, 4317

How to compute the divisors of 4317?

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 4317 by each of the numbers from 1 to 4317 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)

4317 / 1 = 4317 (the remainder is 0, so 1 is a divisor of 4317)
4317 / 2 = 2158.5 (the remainder is 1, so 2 is not a divisor of 4317)
4317 / 3 = 1439 (the remainder is 0, so 3 is a divisor of 4317)
...
4317 / 4316 = 1.0002316960148 (the remainder is 1, so 4316 is not a divisor of 4317)
4317 / 4317 = 1 (the remainder is 0, so 4317 is a divisor of 4317)

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 4317 (i.e. 65.703881163901). 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 $\frac{N}{d} = D$ )

4317 / 1 = 4317 (the remainder is 0, so 1 and 4317 are divisors of 4317)
4317 / 2 = 2158.5 (the remainder is 1, so 2 is not a divisor of 4317)
4317 / 3 = 1439 (the remainder is 0, so 3 and 1439 are divisors of 4317)
...
4317 / 64 = 67.453125 (the remainder is 29, so 64 is not a divisor of 4317)
4317 / 65 = 66.415384615385 (the remainder is 27, so 65 is not a divisor of 4317)