What are the divisors of 5369?

1, 7, 13, 59, 91, 413, 767, 5369

There is a total of 8 positive divisors.
The sum of these divisors is 6720.
The arithmetic mean is 840.

8 odd divisors

1, 7, 13, 59, 91, 413, 767, 5369

How to compute the divisors of 5369?

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 5369 by each of the numbers from 1 to 5369 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)

5369 / 1 = 5369 (the remainder is 0, so 1 is a divisor of 5369)
5369 / 2 = 2684.5 (the remainder is 1, so 2 is not a divisor of 5369)
5369 / 3 = 1789.6666666667 (the remainder is 2, so 3 is not a divisor of 5369)
...
5369 / 5368 = 1.0001862891207 (the remainder is 1, so 5368 is not a divisor of 5369)
5369 / 5369 = 1 (the remainder is 0, so 5369 is a divisor of 5369)

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 5369 (i.e. 73.273460406889). 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 $\frac{N}{d} = D$ )

5369 / 1 = 5369 (the remainder is 0, so 1 and 5369 are divisors of 5369)
5369 / 2 = 2684.5 (the remainder is 1, so 2 is not a divisor of 5369)
5369 / 3 = 1789.6666666667 (the remainder is 2, so 3 is not a divisor of 5369)
...
5369 / 72 = 74.569444444444 (the remainder is 41, so 72 is not a divisor of 5369)
5369 / 73 = 73.547945205479 (the remainder is 40, so 73 is not a divisor of 5369)