What are the divisors of 4369?

1, 17, 257, 4369

There is a total of 4 positive divisors.
The sum of these divisors is 4644.
The arithmetic mean is 1161.

4 odd divisors

1, 17, 257, 4369

How to compute the divisors of 4369?

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 4369 by each of the numbers from 1 to 4369 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)

4369 / 1 = 4369 (the remainder is 0, so 1 is a divisor of 4369)
4369 / 2 = 2184.5 (the remainder is 1, so 2 is not a divisor of 4369)
4369 / 3 = 1456.3333333333 (the remainder is 1, so 3 is not a divisor of 4369)
...
4369 / 4368 = 1.0002289377289 (the remainder is 1, so 4368 is not a divisor of 4369)
4369 / 4369 = 1 (the remainder is 0, so 4369 is a divisor of 4369)

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 4369 (i.e. 66.098411478643). 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 $\frac{N}{d} = D$ )

4369 / 1 = 4369 (the remainder is 0, so 1 and 4369 are divisors of 4369)
4369 / 2 = 2184.5 (the remainder is 1, so 2 is not a divisor of 4369)
4369 / 3 = 1456.3333333333 (the remainder is 1, so 3 is not a divisor of 4369)
...
4369 / 65 = 67.215384615385 (the remainder is 14, so 65 is not a divisor of 4369)
4369 / 66 = 66.19696969697 (the remainder is 13, so 66 is not a divisor of 4369)