What are the divisors of 5196?

1, 2, 3, 4, 6, 12, 433, 866, 1299, 1732, 2598, 5196

There is a total of 12 positive divisors.
The sum of these divisors is 12152.
The arithmetic mean is 1012.6666666667.

8 even divisors

2, 4, 6, 12, 866, 1732, 2598, 5196

4 odd divisors

1, 3, 433, 1299

How to compute the divisors of 5196?

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 5196 by each of the numbers from 1 to 5196 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)

5196 / 1 = 5196 (the remainder is 0, so 1 is a divisor of 5196)
5196 / 2 = 2598 (the remainder is 0, so 2 is a divisor of 5196)
5196 / 3 = 1732 (the remainder is 0, so 3 is a divisor of 5196)
...
5196 / 5195 = 1.0001924927815 (the remainder is 1, so 5195 is not a divisor of 5196)
5196 / 5196 = 1 (the remainder is 0, so 5196 is a divisor of 5196)

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 5196 (i.e. 72.08328516376). 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 $\frac{N}{d} = D$ )

5196 / 1 = 5196 (the remainder is 0, so 1 and 5196 are divisors of 5196)
5196 / 2 = 2598 (the remainder is 0, so 2 and 2598 are divisors of 5196)
5196 / 3 = 1732 (the remainder is 0, so 3 and 1732 are divisors of 5196)
...
5196 / 71 = 73.183098591549 (the remainder is 13, so 71 is not a divisor of 5196)
5196 / 72 = 72.166666666667 (the remainder is 12, so 72 is not a divisor of 5196)