What are the divisors of 5031?

1, 3, 9, 13, 39, 43, 117, 129, 387, 559, 1677, 5031

There is a total of 12 positive divisors.
The sum of these divisors is 8008.
The arithmetic mean is 667.33333333333.

12 odd divisors

1, 3, 9, 13, 39, 43, 117, 129, 387, 559, 1677, 5031

How to compute the divisors of 5031?

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 5031 by each of the numbers from 1 to 5031 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)

5031 / 1 = 5031 (the remainder is 0, so 1 is a divisor of 5031)
5031 / 2 = 2515.5 (the remainder is 1, so 2 is not a divisor of 5031)
5031 / 3 = 1677 (the remainder is 0, so 3 is a divisor of 5031)
...
5031 / 5030 = 1.0001988071571 (the remainder is 1, so 5030 is not a divisor of 5031)
5031 / 5031 = 1 (the remainder is 0, so 5031 is a divisor of 5031)

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 5031 (i.e. 70.929542505221). 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 $\frac{N}{d} = D$ )

5031 / 1 = 5031 (the remainder is 0, so 1 and 5031 are divisors of 5031)
5031 / 2 = 2515.5 (the remainder is 1, so 2 is not a divisor of 5031)
5031 / 3 = 1677 (the remainder is 0, so 3 and 1677 are divisors of 5031)
...
5031 / 69 = 72.913043478261 (the remainder is 63, so 69 is not a divisor of 5031)
5031 / 70 = 71.871428571429 (the remainder is 61, so 70 is not a divisor of 5031)