What are the divisors of 5189?

1, 5189

There is a total of 2 positive divisors.
The sum of these divisors is 5190.
The arithmetic mean is 2595.

2 odd divisors

1, 5189

How to compute the divisors of 5189?

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 5189 by each of the numbers from 1 to 5189 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)

5189 / 1 = 5189 (the remainder is 0, so 1 is a divisor of 5189)
5189 / 2 = 2594.5 (the remainder is 1, so 2 is not a divisor of 5189)
5189 / 3 = 1729.6666666667 (the remainder is 2, so 3 is not a divisor of 5189)
...
5189 / 5188 = 1.0001927525058 (the remainder is 1, so 5188 is not a divisor of 5189)
5189 / 5189 = 1 (the remainder is 0, so 5189 is a divisor of 5189)

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 5189 (i.e. 72.034713853808). 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 $\frac{N}{d} = D$ )

5189 / 1 = 5189 (the remainder is 0, so 1 and 5189 are divisors of 5189)
5189 / 2 = 2594.5 (the remainder is 1, so 2 is not a divisor of 5189)
5189 / 3 = 1729.6666666667 (the remainder is 2, so 3 is not a divisor of 5189)
...
5189 / 71 = 73.084507042254 (the remainder is 6, so 71 is not a divisor of 5189)
5189 / 72 = 72.069444444444 (the remainder is 5, so 72 is not a divisor of 5189)