What are the divisors of 5605?

1, 5, 19, 59, 95, 295, 1121, 5605

There is a total of 8 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 900.

8 odd divisors

1, 5, 19, 59, 95, 295, 1121, 5605

How to compute the divisors of 5605?

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 5605 by each of the numbers from 1 to 5605 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)

5605 / 1 = 5605 (the remainder is 0, so 1 is a divisor of 5605)
5605 / 2 = 2802.5 (the remainder is 1, so 2 is not a divisor of 5605)
5605 / 3 = 1868.3333333333 (the remainder is 1, so 3 is not a divisor of 5605)
...
5605 / 5604 = 1.0001784439686 (the remainder is 1, so 5604 is not a divisor of 5605)
5605 / 5605 = 1 (the remainder is 0, so 5605 is a divisor of 5605)

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 5605 (i.e. 74.866547936979). 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 $\frac{N}{d} = D$ )

5605 / 1 = 5605 (the remainder is 0, so 1 and 5605 are divisors of 5605)
5605 / 2 = 2802.5 (the remainder is 1, so 2 is not a divisor of 5605)
5605 / 3 = 1868.3333333333 (the remainder is 1, so 3 is not a divisor of 5605)
...
5605 / 73 = 76.780821917808 (the remainder is 57, so 73 is not a divisor of 5605)
5605 / 74 = 75.743243243243 (the remainder is 55, so 74 is not a divisor of 5605)