What are the divisors of 5158?

1, 2, 2579, 5158

There is a total of 4 positive divisors.
The sum of these divisors is 7740.
The arithmetic mean is 1935.

2 even divisors

2, 5158

2 odd divisors

1, 2579

How to compute the divisors of 5158?

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 5158 by each of the numbers from 1 to 5158 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)

5158 / 1 = 5158 (the remainder is 0, so 1 is a divisor of 5158)
5158 / 2 = 2579 (the remainder is 0, so 2 is a divisor of 5158)
5158 / 3 = 1719.3333333333 (the remainder is 1, so 3 is not a divisor of 5158)
...
5158 / 5157 = 1.0001939111887 (the remainder is 1, so 5157 is not a divisor of 5158)
5158 / 5158 = 1 (the remainder is 0, so 5158 is a divisor of 5158)

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 5158 (i.e. 71.819217483902). 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 $\frac{N}{d} = D$ )

5158 / 1 = 5158 (the remainder is 0, so 1 and 5158 are divisors of 5158)
5158 / 2 = 2579 (the remainder is 0, so 2 and 2579 are divisors of 5158)
5158 / 3 = 1719.3333333333 (the remainder is 1, so 3 is not a divisor of 5158)
...
5158 / 70 = 73.685714285714 (the remainder is 48, so 70 is not a divisor of 5158)
5158 / 71 = 72.647887323944 (the remainder is 46, so 71 is not a divisor of 5158)