What are the divisors of 5159?

1, 7, 11, 67, 77, 469, 737, 5159

There is a total of 8 positive divisors.
The sum of these divisors is 6528.
The arithmetic mean is 816.

8 odd divisors

1, 7, 11, 67, 77, 469, 737, 5159

How to compute the divisors of 5159?

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 5159 by each of the numbers from 1 to 5159 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)

5159 / 1 = 5159 (the remainder is 0, so 1 is a divisor of 5159)
5159 / 2 = 2579.5 (the remainder is 1, so 2 is not a divisor of 5159)
5159 / 3 = 1719.6666666667 (the remainder is 2, so 3 is not a divisor of 5159)
...
5159 / 5158 = 1.0001938735944 (the remainder is 1, so 5158 is not a divisor of 5159)
5159 / 5159 = 1 (the remainder is 0, so 5159 is a divisor of 5159)

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 5159 (i.e. 71.826179071422). 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 $\frac{N}{d} = D$ )

5159 / 1 = 5159 (the remainder is 0, so 1 and 5159 are divisors of 5159)
5159 / 2 = 2579.5 (the remainder is 1, so 2 is not a divisor of 5159)
5159 / 3 = 1719.6666666667 (the remainder is 2, so 3 is not a divisor of 5159)
...
5159 / 70 = 73.7 (the remainder is 49, so 70 is not a divisor of 5159)
5159 / 71 = 72.661971830986 (the remainder is 47, so 71 is not a divisor of 5159)