What are the divisors of 5641?

1, 5641

There is a total of 2 positive divisors.
The sum of these divisors is 5642.
The arithmetic mean is 2821.

2 odd divisors

1, 5641

How to compute the divisors of 5641?

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 5641 by each of the numbers from 1 to 5641 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)

5641 / 1 = 5641 (the remainder is 0, so 1 is a divisor of 5641)
5641 / 2 = 2820.5 (the remainder is 1, so 2 is not a divisor of 5641)
5641 / 3 = 1880.3333333333 (the remainder is 1, so 3 is not a divisor of 5641)
...
5641 / 5640 = 1.0001773049645 (the remainder is 1, so 5640 is not a divisor of 5641)
5641 / 5641 = 1 (the remainder is 0, so 5641 is a divisor of 5641)

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 5641 (i.e. 75.106590922502). 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 $\frac{N}{d} = D$ )

5641 / 1 = 5641 (the remainder is 0, so 1 and 5641 are divisors of 5641)
5641 / 2 = 2820.5 (the remainder is 1, so 2 is not a divisor of 5641)
5641 / 3 = 1880.3333333333 (the remainder is 1, so 3 is not a divisor of 5641)
...
5641 / 74 = 76.22972972973 (the remainder is 17, so 74 is not a divisor of 5641)
5641 / 75 = 75.213333333333 (the remainder is 16, so 75 is not a divisor of 5641)