What are the divisors of 5137?

1, 11, 467, 5137

There is a total of 4 positive divisors.
The sum of these divisors is 5616.
The arithmetic mean is 1404.

4 odd divisors

1, 11, 467, 5137

How to compute the divisors of 5137?

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 5137 by each of the numbers from 1 to 5137 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)

5137 / 1 = 5137 (the remainder is 0, so 1 is a divisor of 5137)
5137 / 2 = 2568.5 (the remainder is 1, so 2 is not a divisor of 5137)
5137 / 3 = 1712.3333333333 (the remainder is 1, so 3 is not a divisor of 5137)
...
5137 / 5136 = 1.0001947040498 (the remainder is 1, so 5136 is not a divisor of 5137)
5137 / 5137 = 1 (the remainder is 0, so 5137 is a divisor of 5137)

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 5137 (i.e. 71.672867948757). 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 $\frac{N}{d} = D$ )

5137 / 1 = 5137 (the remainder is 0, so 1 and 5137 are divisors of 5137)
5137 / 2 = 2568.5 (the remainder is 1, so 2 is not a divisor of 5137)
5137 / 3 = 1712.3333333333 (the remainder is 1, so 3 is not a divisor of 5137)
...
5137 / 70 = 73.385714285714 (the remainder is 27, so 70 is not a divisor of 5137)
5137 / 71 = 72.352112676056 (the remainder is 25, so 71 is not a divisor of 5137)