What are the divisors of 5148?

1, 2, 3, 4, 6, 9, 11, 12, 13, 18, 22, 26, 33, 36, 39, 44, 52, 66, 78, 99, 117, 132, 143, 156, 198, 234, 286, 396, 429, 468, 572, 858, 1287, 1716, 2574, 5148

There is a total of 36 positive divisors.
The sum of these divisors is 15288.
The arithmetic mean is 424.66666666667.

24 even divisors

2, 4, 6, 12, 18, 22, 26, 36, 44, 52, 66, 78, 132, 156, 198, 234, 286, 396, 468, 572, 858, 1716, 2574, 5148

12 odd divisors

1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429, 1287

How to compute the divisors of 5148?

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 5148 by each of the numbers from 1 to 5148 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)

5148 / 1 = 5148 (the remainder is 0, so 1 is a divisor of 5148)
5148 / 2 = 2574 (the remainder is 0, so 2 is a divisor of 5148)
5148 / 3 = 1716 (the remainder is 0, so 3 is a divisor of 5148)
...
5148 / 5147 = 1.0001942879347 (the remainder is 1, so 5147 is not a divisor of 5148)
5148 / 5148 = 1 (the remainder is 0, so 5148 is a divisor of 5148)

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 5148 (i.e. 71.749564458608). 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 $\frac{N}{d} = D$ )

5148 / 1 = 5148 (the remainder is 0, so 1 and 5148 are divisors of 5148)
5148 / 2 = 2574 (the remainder is 0, so 2 and 2574 are divisors of 5148)
5148 / 3 = 1716 (the remainder is 0, so 3 and 1716 are divisors of 5148)
...
5148 / 70 = 73.542857142857 (the remainder is 38, so 70 is not a divisor of 5148)
5148 / 71 = 72.507042253521 (the remainder is 36, so 71 is not a divisor of 5148)