What are the divisors of 2804?

1, 2, 4, 701, 1402, 2804

There is a total of 6 positive divisors.
The sum of these divisors is 4914.
The arithmetic mean is 819.

4 even divisors

2, 4, 1402, 2804

2 odd divisors

1, 701

How to compute the divisors of 2804?

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 2804 by each of the numbers from 1 to 2804 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)

2804 / 1 = 2804 (the remainder is 0, so 1 is a divisor of 2804)
2804 / 2 = 1402 (the remainder is 0, so 2 is a divisor of 2804)
2804 / 3 = 934.66666666667 (the remainder is 2, so 3 is not a divisor of 2804)
...
2804 / 2803 = 1.0003567606136 (the remainder is 1, so 2803 is not a divisor of 2804)
2804 / 2804 = 1 (the remainder is 0, so 2804 is a divisor of 2804)

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 2804 (i.e. 52.952809179495). 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 $\frac{N}{d} = D$ )

2804 / 1 = 2804 (the remainder is 0, so 1 and 2804 are divisors of 2804)
2804 / 2 = 1402 (the remainder is 0, so 2 and 1402 are divisors of 2804)
2804 / 3 = 934.66666666667 (the remainder is 2, so 3 is not a divisor of 2804)
...
2804 / 51 = 54.980392156863 (the remainder is 50, so 51 is not a divisor of 2804)
2804 / 52 = 53.923076923077 (the remainder is 48, so 52 is not a divisor of 2804)