What are the divisors of 5560?

1, 2, 4, 5, 8, 10, 20, 40, 139, 278, 556, 695, 1112, 1390, 2780, 5560

There is a total of 16 positive divisors.
The sum of these divisors is 12600.
The arithmetic mean is 787.5.

12 even divisors

2, 4, 8, 10, 20, 40, 278, 556, 1112, 1390, 2780, 5560

4 odd divisors

1, 5, 139, 695

How to compute the divisors of 5560?

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 5560 by each of the numbers from 1 to 5560 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)

5560 / 1 = 5560 (the remainder is 0, so 1 is a divisor of 5560)
5560 / 2 = 2780 (the remainder is 0, so 2 is a divisor of 5560)
5560 / 3 = 1853.3333333333 (the remainder is 1, so 3 is not a divisor of 5560)
...
5560 / 5559 = 1.0001798884691 (the remainder is 1, so 5559 is not a divisor of 5560)
5560 / 5560 = 1 (the remainder is 0, so 5560 is a divisor of 5560)

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 5560 (i.e. 74.565407529229). 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 $\frac{N}{d} = D$ )

5560 / 1 = 5560 (the remainder is 0, so 1 and 5560 are divisors of 5560)
5560 / 2 = 2780 (the remainder is 0, so 2 and 2780 are divisors of 5560)
5560 / 3 = 1853.3333333333 (the remainder is 1, so 3 is not a divisor of 5560)
...
5560 / 73 = 76.164383561644 (the remainder is 12, so 73 is not a divisor of 5560)
5560 / 74 = 75.135135135135 (the remainder is 10, so 74 is not a divisor of 5560)