What are the divisors of 2824?

1, 2, 4, 8, 353, 706, 1412, 2824

There is a total of 8 positive divisors.
The sum of these divisors is 5310.
The arithmetic mean is 663.75.

6 even divisors

2, 4, 8, 706, 1412, 2824

2 odd divisors

1, 353

How to compute the divisors of 2824?

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 2824 by each of the numbers from 1 to 2824 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)

2824 / 1 = 2824 (the remainder is 0, so 1 is a divisor of 2824)
2824 / 2 = 1412 (the remainder is 0, so 2 is a divisor of 2824)
2824 / 3 = 941.33333333333 (the remainder is 1, so 3 is not a divisor of 2824)
...
2824 / 2823 = 1.0003542330854 (the remainder is 1, so 2823 is not a divisor of 2824)
2824 / 2824 = 1 (the remainder is 0, so 2824 is a divisor of 2824)

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 2824 (i.e. 53.141321022346). 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 $\frac{N}{d} = D$ )

2824 / 1 = 2824 (the remainder is 0, so 1 and 2824 are divisors of 2824)
2824 / 2 = 1412 (the remainder is 0, so 2 and 1412 are divisors of 2824)
2824 / 3 = 941.33333333333 (the remainder is 1, so 3 is not a divisor of 2824)
...
2824 / 52 = 54.307692307692 (the remainder is 16, so 52 is not a divisor of 2824)
2824 / 53 = 53.283018867925 (the remainder is 15, so 53 is not a divisor of 2824)