What are the divisors of 5289?

1, 3, 41, 43, 123, 129, 1763, 5289

There is a total of 8 positive divisors.
The sum of these divisors is 7392.
The arithmetic mean is 924.

8 odd divisors

1, 3, 41, 43, 123, 129, 1763, 5289

How to compute the divisors of 5289?

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 5289 by each of the numbers from 1 to 5289 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)

5289 / 1 = 5289 (the remainder is 0, so 1 is a divisor of 5289)
5289 / 2 = 2644.5 (the remainder is 1, so 2 is not a divisor of 5289)
5289 / 3 = 1763 (the remainder is 0, so 3 is a divisor of 5289)
...
5289 / 5288 = 1.000189107413 (the remainder is 1, so 5288 is not a divisor of 5289)
5289 / 5289 = 1 (the remainder is 0, so 5289 is a divisor of 5289)

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 5289 (i.e. 72.725511342307). 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 $\frac{N}{d} = D$ )

5289 / 1 = 5289 (the remainder is 0, so 1 and 5289 are divisors of 5289)
5289 / 2 = 2644.5 (the remainder is 1, so 2 is not a divisor of 5289)
5289 / 3 = 1763 (the remainder is 0, so 3 and 1763 are divisors of 5289)
...
5289 / 71 = 74.492957746479 (the remainder is 35, so 71 is not a divisor of 5289)
5289 / 72 = 73.458333333333 (the remainder is 33, so 72 is not a divisor of 5289)