What are the divisors of 5530?

1, 2, 5, 7, 10, 14, 35, 70, 79, 158, 395, 553, 790, 1106, 2765, 5530

There is a total of 16 positive divisors.
The sum of these divisors is 11520.
The arithmetic mean is 720.

8 even divisors

2, 10, 14, 70, 158, 790, 1106, 5530

8 odd divisors

1, 5, 7, 35, 79, 395, 553, 2765

How to compute the divisors of 5530?

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 5530 by each of the numbers from 1 to 5530 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)

5530 / 1 = 5530 (the remainder is 0, so 1 is a divisor of 5530)
5530 / 2 = 2765 (the remainder is 0, so 2 is a divisor of 5530)
5530 / 3 = 1843.3333333333 (the remainder is 1, so 3 is not a divisor of 5530)
...
5530 / 5529 = 1.0001808645325 (the remainder is 1, so 5529 is not a divisor of 5530)
5530 / 5530 = 1 (the remainder is 0, so 5530 is a divisor of 5530)

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 5530 (i.e. 74.363969770313). 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 $\frac{N}{d} = D$ )

5530 / 1 = 5530 (the remainder is 0, so 1 and 5530 are divisors of 5530)
5530 / 2 = 2765 (the remainder is 0, so 2 and 2765 are divisors of 5530)
5530 / 3 = 1843.3333333333 (the remainder is 1, so 3 is not a divisor of 5530)
...
5530 / 73 = 75.753424657534 (the remainder is 55, so 73 is not a divisor of 5530)
5530 / 74 = 74.72972972973 (the remainder is 54, so 74 is not a divisor of 5530)