What are the divisors of 5190?

1, 2, 3, 5, 6, 10, 15, 30, 173, 346, 519, 865, 1038, 1730, 2595, 5190

There is a total of 16 positive divisors.
The sum of these divisors is 12528.
The arithmetic mean is 783.

8 even divisors

2, 6, 10, 30, 346, 1038, 1730, 5190

8 odd divisors

1, 3, 5, 15, 173, 519, 865, 2595

How to compute the divisors of 5190?

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 5190 by each of the numbers from 1 to 5190 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)

5190 / 1 = 5190 (the remainder is 0, so 1 is a divisor of 5190)
5190 / 2 = 2595 (the remainder is 0, so 2 is a divisor of 5190)
5190 / 3 = 1730 (the remainder is 0, so 3 is a divisor of 5190)
...
5190 / 5189 = 1.0001927153594 (the remainder is 1, so 5189 is not a divisor of 5190)
5190 / 5190 = 1 (the remainder is 0, so 5190 is a divisor of 5190)

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 5190 (i.e. 72.041654617312). 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 $\frac{N}{d} = D$ )

5190 / 1 = 5190 (the remainder is 0, so 1 and 5190 are divisors of 5190)
5190 / 2 = 2595 (the remainder is 0, so 2 and 2595 are divisors of 5190)
5190 / 3 = 1730 (the remainder is 0, so 3 and 1730 are divisors of 5190)
...
5190 / 71 = 73.098591549296 (the remainder is 7, so 71 is not a divisor of 5190)
5190 / 72 = 72.083333333333 (the remainder is 6, so 72 is not a divisor of 5190)