What are the divisors of 2682?

1, 2, 3, 6, 9, 18, 149, 298, 447, 894, 1341, 2682

There is a total of 12 positive divisors.
The sum of these divisors is 5850.
The arithmetic mean is 487.5.

6 even divisors

2, 6, 18, 298, 894, 2682

6 odd divisors

1, 3, 9, 149, 447, 1341

How to compute the divisors of 2682?

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 2682 by each of the numbers from 1 to 2682 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)

2682 / 1 = 2682 (the remainder is 0, so 1 is a divisor of 2682)
2682 / 2 = 1341 (the remainder is 0, so 2 is a divisor of 2682)
2682 / 3 = 894 (the remainder is 0, so 3 is a divisor of 2682)
...
2682 / 2681 = 1.0003729951511 (the remainder is 1, so 2681 is not a divisor of 2682)
2682 / 2682 = 1 (the remainder is 0, so 2682 is a divisor of 2682)

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 2682 (i.e. 51.788029504896). 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 $\frac{N}{d} = D$ )

2682 / 1 = 2682 (the remainder is 0, so 1 and 2682 are divisors of 2682)
2682 / 2 = 1341 (the remainder is 0, so 2 and 1341 are divisors of 2682)
2682 / 3 = 894 (the remainder is 0, so 3 and 894 are divisors of 2682)
...
2682 / 50 = 53.64 (the remainder is 32, so 50 is not a divisor of 2682)
2682 / 51 = 52.588235294118 (the remainder is 30, so 51 is not a divisor of 2682)