What are the divisors of 5525?

1, 5, 13, 17, 25, 65, 85, 221, 325, 425, 1105, 5525

There is a total of 12 positive divisors.
The sum of these divisors is 7812.
The arithmetic mean is 651.

12 odd divisors

1, 5, 13, 17, 25, 65, 85, 221, 325, 425, 1105, 5525

How to compute the divisors of 5525?

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 5525 by each of the numbers from 1 to 5525 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)

5525 / 1 = 5525 (the remainder is 0, so 1 is a divisor of 5525)
5525 / 2 = 2762.5 (the remainder is 1, so 2 is not a divisor of 5525)
5525 / 3 = 1841.6666666667 (the remainder is 2, so 3 is not a divisor of 5525)
...
5525 / 5524 = 1.0001810282404 (the remainder is 1, so 5524 is not a divisor of 5525)
5525 / 5525 = 1 (the remainder is 0, so 5525 is a divisor of 5525)

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 5525 (i.e. 74.330343736593). 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 $\frac{N}{d} = D$ )

5525 / 1 = 5525 (the remainder is 0, so 1 and 5525 are divisors of 5525)
5525 / 2 = 2762.5 (the remainder is 1, so 2 is not a divisor of 5525)
5525 / 3 = 1841.6666666667 (the remainder is 2, so 3 is not a divisor of 5525)
...
5525 / 73 = 75.684931506849 (the remainder is 50, so 73 is not a divisor of 5525)
5525 / 74 = 74.662162162162 (the remainder is 49, so 74 is not a divisor of 5525)