What are the divisors of 4635?

1, 3, 5, 9, 15, 45, 103, 309, 515, 927, 1545, 4635

There is a total of 12 positive divisors.
The sum of these divisors is 8112.
The arithmetic mean is 676.

12 odd divisors

1, 3, 5, 9, 15, 45, 103, 309, 515, 927, 1545, 4635

How to compute the divisors of 4635?

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 4635 by each of the numbers from 1 to 4635 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)

4635 / 1 = 4635 (the remainder is 0, so 1 is a divisor of 4635)
4635 / 2 = 2317.5 (the remainder is 1, so 2 is not a divisor of 4635)
4635 / 3 = 1545 (the remainder is 0, so 3 is a divisor of 4635)
...
4635 / 4634 = 1.0002157962883 (the remainder is 1, so 4634 is not a divisor of 4635)
4635 / 4635 = 1 (the remainder is 0, so 4635 is a divisor of 4635)

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 4635 (i.e. 68.080834307461). 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 $\frac{N}{d} = D$ )

4635 / 1 = 4635 (the remainder is 0, so 1 and 4635 are divisors of 4635)
4635 / 2 = 2317.5 (the remainder is 1, so 2 is not a divisor of 4635)
4635 / 3 = 1545 (the remainder is 0, so 3 and 1545 are divisors of 4635)
...
4635 / 67 = 69.179104477612 (the remainder is 12, so 67 is not a divisor of 4635)
4635 / 68 = 68.161764705882 (the remainder is 11, so 68 is not a divisor of 4635)