What are the divisors of 5139?

1, 3, 9, 571, 1713, 5139

There is a total of 6 positive divisors.
The sum of these divisors is 7436.
The arithmetic mean is 1239.3333333333.

6 odd divisors

1, 3, 9, 571, 1713, 5139

How to compute the divisors of 5139?

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 5139 by each of the numbers from 1 to 5139 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)

5139 / 1 = 5139 (the remainder is 0, so 1 is a divisor of 5139)
5139 / 2 = 2569.5 (the remainder is 1, so 2 is not a divisor of 5139)
5139 / 3 = 1713 (the remainder is 0, so 3 is a divisor of 5139)
...
5139 / 5138 = 1.00019462826 (the remainder is 1, so 5138 is not a divisor of 5139)
5139 / 5139 = 1 (the remainder is 0, so 5139 is a divisor of 5139)

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 5139 (i.e. 71.686818872091). 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 $\frac{N}{d} = D$ )

5139 / 1 = 5139 (the remainder is 0, so 1 and 5139 are divisors of 5139)
5139 / 2 = 2569.5 (the remainder is 1, so 2 is not a divisor of 5139)
5139 / 3 = 1713 (the remainder is 0, so 3 and 1713 are divisors of 5139)
...
5139 / 70 = 73.414285714286 (the remainder is 29, so 70 is not a divisor of 5139)
5139 / 71 = 72.380281690141 (the remainder is 27, so 71 is not a divisor of 5139)