What are the divisors of 5568?

1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 32, 48, 58, 64, 87, 96, 116, 174, 192, 232, 348, 464, 696, 928, 1392, 1856, 2784, 5568

There is a total of 28 positive divisors.
The sum of these divisors is 15240.
The arithmetic mean is 544.28571428571.

24 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 58, 64, 96, 116, 174, 192, 232, 348, 464, 696, 928, 1392, 1856, 2784, 5568

4 odd divisors

1, 3, 29, 87

How to compute the divisors of 5568?

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 5568 by each of the numbers from 1 to 5568 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)

5568 / 1 = 5568 (the remainder is 0, so 1 is a divisor of 5568)
5568 / 2 = 2784 (the remainder is 0, so 2 is a divisor of 5568)
5568 / 3 = 1856 (the remainder is 0, so 3 is a divisor of 5568)
...
5568 / 5567 = 1.0001796299623 (the remainder is 1, so 5567 is not a divisor of 5568)
5568 / 5568 = 1 (the remainder is 0, so 5568 is a divisor of 5568)

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 5568 (i.e. 74.619032424711). 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 $\frac{N}{d} = D$ )

5568 / 1 = 5568 (the remainder is 0, so 1 and 5568 are divisors of 5568)
5568 / 2 = 2784 (the remainder is 0, so 2 and 2784 are divisors of 5568)
5568 / 3 = 1856 (the remainder is 0, so 3 and 1856 are divisors of 5568)
...
5568 / 73 = 76.27397260274 (the remainder is 20, so 73 is not a divisor of 5568)
5568 / 74 = 75.243243243243 (the remainder is 18, so 74 is not a divisor of 5568)