What are the divisors of 5659?

1, 5659

There is a total of 2 positive divisors.
The sum of these divisors is 5660.
The arithmetic mean is 2830.

2 odd divisors

1, 5659

How to compute the divisors of 5659?

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 5659 by each of the numbers from 1 to 5659 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)

5659 / 1 = 5659 (the remainder is 0, so 1 is a divisor of 5659)
5659 / 2 = 2829.5 (the remainder is 1, so 2 is not a divisor of 5659)
5659 / 3 = 1886.3333333333 (the remainder is 1, so 3 is not a divisor of 5659)
...
5659 / 5658 = 1.0001767408978 (the remainder is 1, so 5658 is not a divisor of 5659)
5659 / 5659 = 1 (the remainder is 0, so 5659 is a divisor of 5659)

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 5659 (i.e. 75.226325179421). 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 $\frac{N}{d} = D$ )

5659 / 1 = 5659 (the remainder is 0, so 1 and 5659 are divisors of 5659)
5659 / 2 = 2829.5 (the remainder is 1, so 2 is not a divisor of 5659)
5659 / 3 = 1886.3333333333 (the remainder is 1, so 3 is not a divisor of 5659)
...
5659 / 74 = 76.472972972973 (the remainder is 35, so 74 is not a divisor of 5659)
5659 / 75 = 75.453333333333 (the remainder is 34, so 75 is not a divisor of 5659)