What are the divisors of 2884?

1, 2, 4, 7, 14, 28, 103, 206, 412, 721, 1442, 2884

There is a total of 12 positive divisors.
The sum of these divisors is 5824.
The arithmetic mean is 485.33333333333.

8 even divisors

2, 4, 14, 28, 206, 412, 1442, 2884

4 odd divisors

1, 7, 103, 721

How to compute the divisors of 2884?

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 2884 by each of the numbers from 1 to 2884 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)

2884 / 1 = 2884 (the remainder is 0, so 1 is a divisor of 2884)
2884 / 2 = 1442 (the remainder is 0, so 2 is a divisor of 2884)
2884 / 3 = 961.33333333333 (the remainder is 1, so 3 is not a divisor of 2884)
...
2884 / 2883 = 1.0003468609088 (the remainder is 1, so 2883 is not a divisor of 2884)
2884 / 2884 = 1 (the remainder is 0, so 2884 is a divisor of 2884)

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 2884 (i.e. 53.70288632839). 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 $\frac{N}{d} = D$ )

2884 / 1 = 2884 (the remainder is 0, so 1 and 2884 are divisors of 2884)
2884 / 2 = 1442 (the remainder is 0, so 2 and 1442 are divisors of 2884)
2884 / 3 = 961.33333333333 (the remainder is 1, so 3 is not a divisor of 2884)
...
2884 / 52 = 55.461538461538 (the remainder is 24, so 52 is not a divisor of 2884)
2884 / 53 = 54.415094339623 (the remainder is 22, so 53 is not a divisor of 2884)