What are the divisors of 5676?

1, 2, 3, 4, 6, 11, 12, 22, 33, 43, 44, 66, 86, 129, 132, 172, 258, 473, 516, 946, 1419, 1892, 2838, 5676

There is a total of 24 positive divisors.
The sum of these divisors is 14784.
The arithmetic mean is 616.

16 even divisors

2, 4, 6, 12, 22, 44, 66, 86, 132, 172, 258, 516, 946, 1892, 2838, 5676

8 odd divisors

1, 3, 11, 33, 43, 129, 473, 1419

How to compute the divisors of 5676?

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 5676 by each of the numbers from 1 to 5676 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)

5676 / 1 = 5676 (the remainder is 0, so 1 is a divisor of 5676)
5676 / 2 = 2838 (the remainder is 0, so 2 is a divisor of 5676)
5676 / 3 = 1892 (the remainder is 0, so 3 is a divisor of 5676)
...
5676 / 5675 = 1.0001762114537 (the remainder is 1, so 5675 is not a divisor of 5676)
5676 / 5676 = 1 (the remainder is 0, so 5676 is a divisor of 5676)

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 5676 (i.e. 75.339232807349). 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 $\frac{N}{d} = D$ )

5676 / 1 = 5676 (the remainder is 0, so 1 and 5676 are divisors of 5676)
5676 / 2 = 2838 (the remainder is 0, so 2 and 2838 are divisors of 5676)
5676 / 3 = 1892 (the remainder is 0, so 3 and 1892 are divisors of 5676)
...
5676 / 74 = 76.702702702703 (the remainder is 52, so 74 is not a divisor of 5676)
5676 / 75 = 75.68 (the remainder is 51, so 75 is not a divisor of 5676)