What are the divisors of 5691?

1, 3, 7, 21, 271, 813, 1897, 5691

There is a total of 8 positive divisors.
The sum of these divisors is 8704.
The arithmetic mean is 1088.

8 odd divisors

1, 3, 7, 21, 271, 813, 1897, 5691

How to compute the divisors of 5691?

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 5691 by each of the numbers from 1 to 5691 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)

5691 / 1 = 5691 (the remainder is 0, so 1 is a divisor of 5691)
5691 / 2 = 2845.5 (the remainder is 1, so 2 is not a divisor of 5691)
5691 / 3 = 1897 (the remainder is 0, so 3 is a divisor of 5691)
...
5691 / 5690 = 1.0001757469244 (the remainder is 1, so 5690 is not a divisor of 5691)
5691 / 5691 = 1 (the remainder is 0, so 5691 is a divisor of 5691)

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 5691 (i.e. 75.438716850169). 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 $\frac{N}{d} = D$ )

5691 / 1 = 5691 (the remainder is 0, so 1 and 5691 are divisors of 5691)
5691 / 2 = 2845.5 (the remainder is 1, so 2 is not a divisor of 5691)
5691 / 3 = 1897 (the remainder is 0, so 3 and 1897 are divisors of 5691)
...
5691 / 74 = 76.905405405405 (the remainder is 67, so 74 is not a divisor of 5691)
5691 / 75 = 75.88 (the remainder is 66, so 75 is not a divisor of 5691)