What are the divisors of 2848?

1, 2, 4, 8, 16, 32, 89, 178, 356, 712, 1424, 2848

There is a total of 12 positive divisors.
The sum of these divisors is 5670.
The arithmetic mean is 472.5.

10 even divisors

2, 4, 8, 16, 32, 178, 356, 712, 1424, 2848

2 odd divisors

1, 89

How to compute the divisors of 2848?

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 2848 by each of the numbers from 1 to 2848 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)

2848 / 1 = 2848 (the remainder is 0, so 1 is a divisor of 2848)
2848 / 2 = 1424 (the remainder is 0, so 2 is a divisor of 2848)
2848 / 3 = 949.33333333333 (the remainder is 1, so 3 is not a divisor of 2848)
...
2848 / 2847 = 1.0003512469266 (the remainder is 1, so 2847 is not a divisor of 2848)
2848 / 2848 = 1 (the remainder is 0, so 2848 is a divisor of 2848)

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 2848 (i.e. 53.366656256505). 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 $\frac{N}{d} = D$ )

2848 / 1 = 2848 (the remainder is 0, so 1 and 2848 are divisors of 2848)
2848 / 2 = 1424 (the remainder is 0, so 2 and 1424 are divisors of 2848)
2848 / 3 = 949.33333333333 (the remainder is 1, so 3 is not a divisor of 2848)
...
2848 / 52 = 54.769230769231 (the remainder is 40, so 52 is not a divisor of 2848)
2848 / 53 = 53.735849056604 (the remainder is 39, so 53 is not a divisor of 2848)