What are the divisors of 5123?

1, 47, 109, 5123

There is a total of 4 positive divisors.
The sum of these divisors is 5280.
The arithmetic mean is 1320.

4 odd divisors

1, 47, 109, 5123

How to compute the divisors of 5123?

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 5123 by each of the numbers from 1 to 5123 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)

5123 / 1 = 5123 (the remainder is 0, so 1 is a divisor of 5123)
5123 / 2 = 2561.5 (the remainder is 1, so 2 is not a divisor of 5123)
5123 / 3 = 1707.6666666667 (the remainder is 2, so 3 is not a divisor of 5123)
...
5123 / 5122 = 1.0001952362358 (the remainder is 1, so 5122 is not a divisor of 5123)
5123 / 5123 = 1 (the remainder is 0, so 5123 is a divisor of 5123)

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 5123 (i.e. 71.57513534741). 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 $\frac{N}{d} = D$ )

5123 / 1 = 5123 (the remainder is 0, so 1 and 5123 are divisors of 5123)
5123 / 2 = 2561.5 (the remainder is 1, so 2 is not a divisor of 5123)
5123 / 3 = 1707.6666666667 (the remainder is 2, so 3 is not a divisor of 5123)
...
5123 / 70 = 73.185714285714 (the remainder is 13, so 70 is not a divisor of 5123)
5123 / 71 = 72.154929577465 (the remainder is 11, so 71 is not a divisor of 5123)