What are the divisors of 2708?

1, 2, 4, 677, 1354, 2708

There is a total of 6 positive divisors.
The sum of these divisors is 4746.
The arithmetic mean is 791.

4 even divisors

2, 4, 1354, 2708

2 odd divisors

1, 677

How to compute the divisors of 2708?

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 2708 by each of the numbers from 1 to 2708 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)

2708 / 1 = 2708 (the remainder is 0, so 1 is a divisor of 2708)
2708 / 2 = 1354 (the remainder is 0, so 2 is a divisor of 2708)
2708 / 3 = 902.66666666667 (the remainder is 2, so 3 is not a divisor of 2708)
...
2708 / 2707 = 1.0003694126339 (the remainder is 1, so 2707 is not a divisor of 2708)
2708 / 2708 = 1 (the remainder is 0, so 2708 is a divisor of 2708)

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 2708 (i.e. 52.038447325031). 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 $\frac{N}{d} = D$ )

2708 / 1 = 2708 (the remainder is 0, so 1 and 2708 are divisors of 2708)
2708 / 2 = 1354 (the remainder is 0, so 2 and 1354 are divisors of 2708)
2708 / 3 = 902.66666666667 (the remainder is 2, so 3 is not a divisor of 2708)
...
2708 / 51 = 53.098039215686 (the remainder is 5, so 51 is not a divisor of 2708)
2708 / 52 = 52.076923076923 (the remainder is 4, so 52 is not a divisor of 2708)