What are the divisors of 5502?

1, 2, 3, 6, 7, 14, 21, 42, 131, 262, 393, 786, 917, 1834, 2751, 5502

There is a total of 16 positive divisors.
The sum of these divisors is 12672.
The arithmetic mean is 792.

8 even divisors

2, 6, 14, 42, 262, 786, 1834, 5502

8 odd divisors

1, 3, 7, 21, 131, 393, 917, 2751

How to compute the divisors of 5502?

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 5502 by each of the numbers from 1 to 5502 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)

5502 / 1 = 5502 (the remainder is 0, so 1 is a divisor of 5502)
5502 / 2 = 2751 (the remainder is 0, so 2 is a divisor of 5502)
5502 / 3 = 1834 (the remainder is 0, so 3 is a divisor of 5502)
...
5502 / 5501 = 1.00018178513 (the remainder is 1, so 5501 is not a divisor of 5502)
5502 / 5502 = 1 (the remainder is 0, so 5502 is a divisor of 5502)

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 5502 (i.e. 74.175467642611). 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 $\frac{N}{d} = D$ )

5502 / 1 = 5502 (the remainder is 0, so 1 and 5502 are divisors of 5502)
5502 / 2 = 2751 (the remainder is 0, so 2 and 2751 are divisors of 5502)
5502 / 3 = 1834 (the remainder is 0, so 3 and 1834 are divisors of 5502)
...
5502 / 73 = 75.369863013699 (the remainder is 27, so 73 is not a divisor of 5502)
5502 / 74 = 74.351351351351 (the remainder is 26, so 74 is not a divisor of 5502)