What are the divisors of 5699?

1, 41, 139, 5699

There is a total of 4 positive divisors.
The sum of these divisors is 5880.
The arithmetic mean is 1470.

4 odd divisors

1, 41, 139, 5699

How to compute the divisors of 5699?

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 5699 by each of the numbers from 1 to 5699 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)

5699 / 1 = 5699 (the remainder is 0, so 1 is a divisor of 5699)
5699 / 2 = 2849.5 (the remainder is 1, so 2 is not a divisor of 5699)
5699 / 3 = 1899.6666666667 (the remainder is 2, so 3 is not a divisor of 5699)
...
5699 / 5698 = 1.0001755001755 (the remainder is 1, so 5698 is not a divisor of 5699)
5699 / 5699 = 1 (the remainder is 0, so 5699 is a divisor of 5699)

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 5699 (i.e. 75.491721400429). 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 $\frac{N}{d} = D$ )

5699 / 1 = 5699 (the remainder is 0, so 1 and 5699 are divisors of 5699)
5699 / 2 = 2849.5 (the remainder is 1, so 2 is not a divisor of 5699)
5699 / 3 = 1899.6666666667 (the remainder is 2, so 3 is not a divisor of 5699)
...
5699 / 74 = 77.013513513514 (the remainder is 1, so 74 is not a divisor of 5699)
5699 / 75 = 75.986666666667 (the remainder is 74, so 75 is not a divisor of 5699)