What are the divisors of 5681?

1, 13, 19, 23, 247, 299, 437, 5681

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

8 odd divisors

1, 13, 19, 23, 247, 299, 437, 5681

How to compute the divisors of 5681?

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 5681 by each of the numbers from 1 to 5681 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)

5681 / 1 = 5681 (the remainder is 0, so 1 is a divisor of 5681)
5681 / 2 = 2840.5 (the remainder is 1, so 2 is not a divisor of 5681)
5681 / 3 = 1893.6666666667 (the remainder is 2, so 3 is not a divisor of 5681)
...
5681 / 5680 = 1.000176056338 (the remainder is 1, so 5680 is not a divisor of 5681)
5681 / 5681 = 1 (the remainder is 0, so 5681 is a divisor of 5681)

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 5681 (i.e. 75.372408744845). 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 $\frac{N}{d} = D$ )

5681 / 1 = 5681 (the remainder is 0, so 1 and 5681 are divisors of 5681)
5681 / 2 = 2840.5 (the remainder is 1, so 2 is not a divisor of 5681)
5681 / 3 = 1893.6666666667 (the remainder is 2, so 3 is not a divisor of 5681)
...
5681 / 74 = 76.77027027027 (the remainder is 57, so 74 is not a divisor of 5681)
5681 / 75 = 75.746666666667 (the remainder is 56, so 75 is not a divisor of 5681)