What are the divisors of 2756?

1, 2, 4, 13, 26, 52, 53, 106, 212, 689, 1378, 2756

There is a total of 12 positive divisors.
The sum of these divisors is 5292.
The arithmetic mean is 441.

8 even divisors

2, 4, 26, 52, 106, 212, 1378, 2756

4 odd divisors

1, 13, 53, 689

How to compute the divisors of 2756?

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 2756 by each of the numbers from 1 to 2756 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)

2756 / 1 = 2756 (the remainder is 0, so 1 is a divisor of 2756)
2756 / 2 = 1378 (the remainder is 0, so 2 is a divisor of 2756)
2756 / 3 = 918.66666666667 (the remainder is 2, so 3 is not a divisor of 2756)
...
2756 / 2755 = 1.0003629764065 (the remainder is 1, so 2755 is not a divisor of 2756)
2756 / 2756 = 1 (the remainder is 0, so 2756 is a divisor of 2756)

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 2756 (i.e. 52.497618993627). 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 $\frac{N}{d} = D$ )

2756 / 1 = 2756 (the remainder is 0, so 1 and 2756 are divisors of 2756)
2756 / 2 = 1378 (the remainder is 0, so 2 and 1378 are divisors of 2756)
2756 / 3 = 918.66666666667 (the remainder is 2, so 3 is not a divisor of 2756)
...
2756 / 51 = 54.039215686275 (the remainder is 2, so 51 is not a divisor of 2756)
2756 / 52 = 53 (the remainder is 0, so 52 and 53 are divisors of 2756)