What are the divisors of 4505?

1, 5, 17, 53, 85, 265, 901, 4505

There is a total of 8 positive divisors.
The sum of these divisors is 5832.
The arithmetic mean is 729.

8 odd divisors

1, 5, 17, 53, 85, 265, 901, 4505

How to compute the divisors of 4505?

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 4505 by each of the numbers from 1 to 4505 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)

4505 / 1 = 4505 (the remainder is 0, so 1 is a divisor of 4505)
4505 / 2 = 2252.5 (the remainder is 1, so 2 is not a divisor of 4505)
4505 / 3 = 1501.6666666667 (the remainder is 2, so 3 is not a divisor of 4505)
...
4505 / 4504 = 1.0002220248668 (the remainder is 1, so 4504 is not a divisor of 4505)
4505 / 4505 = 1 (the remainder is 0, so 4505 is a divisor of 4505)

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 4505 (i.e. 67.119296778199). 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 $\frac{N}{d} = D$ )

4505 / 1 = 4505 (the remainder is 0, so 1 and 4505 are divisors of 4505)
4505 / 2 = 2252.5 (the remainder is 1, so 2 is not a divisor of 4505)
4505 / 3 = 1501.6666666667 (the remainder is 2, so 3 is not a divisor of 4505)
...
4505 / 66 = 68.257575757576 (the remainder is 17, so 66 is not a divisor of 4505)
4505 / 67 = 67.238805970149 (the remainder is 16, so 67 is not a divisor of 4505)