What are the divisors of 3553?

1, 11, 17, 19, 187, 209, 323, 3553

There is a total of 8 positive divisors.
The sum of these divisors is 4320.
The arithmetic mean is 540.

8 odd divisors

1, 11, 17, 19, 187, 209, 323, 3553

How to compute the divisors of 3553?

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 3553 by each of the numbers from 1 to 3553 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)

3553 / 1 = 3553 (the remainder is 0, so 1 is a divisor of 3553)
3553 / 2 = 1776.5 (the remainder is 1, so 2 is not a divisor of 3553)
3553 / 3 = 1184.3333333333 (the remainder is 1, so 3 is not a divisor of 3553)
...
3553 / 3552 = 1.0002815315315 (the remainder is 1, so 3552 is not a divisor of 3553)
3553 / 3553 = 1 (the remainder is 0, so 3553 is a divisor of 3553)

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 3553 (i.e. 59.607046563305). 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 $\frac{N}{d} = D$ )

3553 / 1 = 3553 (the remainder is 0, so 1 and 3553 are divisors of 3553)
3553 / 2 = 1776.5 (the remainder is 1, so 2 is not a divisor of 3553)
3553 / 3 = 1184.3333333333 (the remainder is 1, so 3 is not a divisor of 3553)
...
3553 / 58 = 61.258620689655 (the remainder is 15, so 58 is not a divisor of 3553)
3553 / 59 = 60.220338983051 (the remainder is 13, so 59 is not a divisor of 3553)