What are the divisors of 2685?

1, 3, 5, 15, 179, 537, 895, 2685

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

8 odd divisors

1, 3, 5, 15, 179, 537, 895, 2685

How to compute the divisors of 2685?

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 2685 by each of the numbers from 1 to 2685 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)

2685 / 1 = 2685 (the remainder is 0, so 1 is a divisor of 2685)
2685 / 2 = 1342.5 (the remainder is 1, so 2 is not a divisor of 2685)
2685 / 3 = 895 (the remainder is 0, so 3 is a divisor of 2685)
...
2685 / 2684 = 1.0003725782414 (the remainder is 1, so 2684 is not a divisor of 2685)
2685 / 2685 = 1 (the remainder is 0, so 2685 is a divisor of 2685)

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 2685 (i.e. 51.816985632126). 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 $\frac{N}{d} = D$ )

2685 / 1 = 2685 (the remainder is 0, so 1 and 2685 are divisors of 2685)
2685 / 2 = 1342.5 (the remainder is 1, so 2 is not a divisor of 2685)
2685 / 3 = 895 (the remainder is 0, so 3 and 895 are divisors of 2685)
...
2685 / 50 = 53.7 (the remainder is 35, so 50 is not a divisor of 2685)
2685 / 51 = 52.647058823529 (the remainder is 33, so 51 is not a divisor of 2685)