What are the divisors of 2676?

1, 2, 3, 4, 6, 12, 223, 446, 669, 892, 1338, 2676

There is a total of 12 positive divisors.
The sum of these divisors is 6272.
The arithmetic mean is 522.66666666667.

8 even divisors

2, 4, 6, 12, 446, 892, 1338, 2676

4 odd divisors

1, 3, 223, 669

How to compute the divisors of 2676?

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 2676 by each of the numbers from 1 to 2676 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)

2676 / 1 = 2676 (the remainder is 0, so 1 is a divisor of 2676)
2676 / 2 = 1338 (the remainder is 0, so 2 is a divisor of 2676)
2676 / 3 = 892 (the remainder is 0, so 3 is a divisor of 2676)
...
2676 / 2675 = 1.0003738317757 (the remainder is 1, so 2675 is not a divisor of 2676)
2676 / 2676 = 1 (the remainder is 0, so 2676 is a divisor of 2676)

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 2676 (i.e. 51.73006862551). 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 $\frac{N}{d} = D$ )

2676 / 1 = 2676 (the remainder is 0, so 1 and 2676 are divisors of 2676)
2676 / 2 = 1338 (the remainder is 0, so 2 and 1338 are divisors of 2676)
2676 / 3 = 892 (the remainder is 0, so 3 and 892 are divisors of 2676)
...
2676 / 50 = 53.52 (the remainder is 26, so 50 is not a divisor of 2676)
2676 / 51 = 52.470588235294 (the remainder is 24, so 51 is not a divisor of 2676)