What are the divisors of 5207?

1, 41, 127, 5207

There is a total of 4 positive divisors.
The sum of these divisors is 5376.
The arithmetic mean is 1344.

4 odd divisors

1, 41, 127, 5207

How to compute the divisors of 5207?

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 5207 by each of the numbers from 1 to 5207 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)

5207 / 1 = 5207 (the remainder is 0, so 1 is a divisor of 5207)
5207 / 2 = 2603.5 (the remainder is 1, so 2 is not a divisor of 5207)
5207 / 3 = 1735.6666666667 (the remainder is 2, so 3 is not a divisor of 5207)
...
5207 / 5206 = 1.0001920860546 (the remainder is 1, so 5206 is not a divisor of 5207)
5207 / 5207 = 1 (the remainder is 0, so 5207 is a divisor of 5207)

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 5207 (i.e. 72.159545453114). 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 $\frac{N}{d} = D$ )

5207 / 1 = 5207 (the remainder is 0, so 1 and 5207 are divisors of 5207)
5207 / 2 = 2603.5 (the remainder is 1, so 2 is not a divisor of 5207)
5207 / 3 = 1735.6666666667 (the remainder is 2, so 3 is not a divisor of 5207)
...
5207 / 71 = 73.338028169014 (the remainder is 24, so 71 is not a divisor of 5207)
5207 / 72 = 72.319444444444 (the remainder is 23, so 72 is not a divisor of 5207)