What are the divisors of 5195?

1, 5, 1039, 5195

There is a total of 4 positive divisors.
The sum of these divisors is 6240.
The arithmetic mean is 1560.

4 odd divisors

1, 5, 1039, 5195

How to compute the divisors of 5195?

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 5195 by each of the numbers from 1 to 5195 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)

5195 / 1 = 5195 (the remainder is 0, so 1 is a divisor of 5195)
5195 / 2 = 2597.5 (the remainder is 1, so 2 is not a divisor of 5195)
5195 / 3 = 1731.6666666667 (the remainder is 2, so 3 is not a divisor of 5195)
...
5195 / 5194 = 1.0001925298421 (the remainder is 1, so 5194 is not a divisor of 5195)
5195 / 5195 = 1 (the remainder is 0, so 5195 is a divisor of 5195)

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 5195 (i.e. 72.07634840917). 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 $\frac{N}{d} = D$ )

5195 / 1 = 5195 (the remainder is 0, so 1 and 5195 are divisors of 5195)
5195 / 2 = 2597.5 (the remainder is 1, so 2 is not a divisor of 5195)
5195 / 3 = 1731.6666666667 (the remainder is 2, so 3 is not a divisor of 5195)
...
5195 / 71 = 73.169014084507 (the remainder is 12, so 71 is not a divisor of 5195)
5195 / 72 = 72.152777777778 (the remainder is 11, so 72 is not a divisor of 5195)