What are the divisors of 2856?

1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 21, 24, 28, 34, 42, 51, 56, 68, 84, 102, 119, 136, 168, 204, 238, 357, 408, 476, 714, 952, 1428, 2856

There is a total of 32 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 270.

24 even divisors

2, 4, 6, 8, 12, 14, 24, 28, 34, 42, 56, 68, 84, 102, 136, 168, 204, 238, 408, 476, 714, 952, 1428, 2856

8 odd divisors

1, 3, 7, 17, 21, 51, 119, 357

How to compute the divisors of 2856?

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 2856 by each of the numbers from 1 to 2856 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)

2856 / 1 = 2856 (the remainder is 0, so 1 is a divisor of 2856)
2856 / 2 = 1428 (the remainder is 0, so 2 is a divisor of 2856)
2856 / 3 = 952 (the remainder is 0, so 3 is a divisor of 2856)
...
2856 / 2855 = 1.000350262697 (the remainder is 1, so 2855 is not a divisor of 2856)
2856 / 2856 = 1 (the remainder is 0, so 2856 is a divisor of 2856)

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 2856 (i.e. 53.44155686355). 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 $\frac{N}{d} = D$ )

2856 / 1 = 2856 (the remainder is 0, so 1 and 2856 are divisors of 2856)
2856 / 2 = 1428 (the remainder is 0, so 2 and 1428 are divisors of 2856)
2856 / 3 = 952 (the remainder is 0, so 3 and 952 are divisors of 2856)
...
2856 / 52 = 54.923076923077 (the remainder is 48, so 52 is not a divisor of 2856)
2856 / 53 = 53.88679245283 (the remainder is 47, so 53 is not a divisor of 2856)