What are the divisors of 2704?

1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704

There is a total of 15 positive divisors.
The sum of these divisors is 5673.
The arithmetic mean is 378.2.

12 even divisors

2, 4, 8, 16, 26, 52, 104, 208, 338, 676, 1352, 2704

3 odd divisors

1, 13, 169

How to compute the divisors of 2704?

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 2704 by each of the numbers from 1 to 2704 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)

2704 / 1 = 2704 (the remainder is 0, so 1 is a divisor of 2704)
2704 / 2 = 1352 (the remainder is 0, so 2 is a divisor of 2704)
2704 / 3 = 901.33333333333 (the remainder is 1, so 3 is not a divisor of 2704)
...
2704 / 2703 = 1.0003699593045 (the remainder is 1, so 2703 is not a divisor of 2704)
2704 / 2704 = 1 (the remainder is 0, so 2704 is a divisor of 2704)

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 2704 (i.e. 52). 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 $\frac{N}{d} = D$ )

2704 / 1 = 2704 (the remainder is 0, so 1 and 2704 are divisors of 2704)
2704 / 2 = 1352 (the remainder is 0, so 2 and 1352 are divisors of 2704)
2704 / 3 = 901.33333333333 (the remainder is 1, so 3 is not a divisor of 2704)
...
2704 / 51 = 53.019607843137 (the remainder is 1, so 51 is not a divisor of 2704)
2704 / 52 = 52 (the remainder is 0, so 52 and 52 are divisors of 2704)