What are the divisors of 2872?

1, 2, 4, 8, 359, 718, 1436, 2872

There is a total of 8 positive divisors.
The sum of these divisors is 5400.
The arithmetic mean is 675.

6 even divisors

2, 4, 8, 718, 1436, 2872

2 odd divisors

1, 359

How to compute the divisors of 2872?

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 2872 by each of the numbers from 1 to 2872 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)

2872 / 1 = 2872 (the remainder is 0, so 1 is a divisor of 2872)
2872 / 2 = 1436 (the remainder is 0, so 2 is a divisor of 2872)
2872 / 3 = 957.33333333333 (the remainder is 1, so 3 is not a divisor of 2872)
...
2872 / 2871 = 1.0003483106931 (the remainder is 1, so 2871 is not a divisor of 2872)
2872 / 2872 = 1 (the remainder is 0, so 2872 is a divisor of 2872)

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 2872 (i.e. 53.591044027897). 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 $\frac{N}{d} = D$ )

2872 / 1 = 2872 (the remainder is 0, so 1 and 2872 are divisors of 2872)
2872 / 2 = 1436 (the remainder is 0, so 2 and 1436 are divisors of 2872)
2872 / 3 = 957.33333333333 (the remainder is 1, so 3 is not a divisor of 2872)
...
2872 / 52 = 55.230769230769 (the remainder is 12, so 52 is not a divisor of 2872)
2872 / 53 = 54.188679245283 (the remainder is 10, so 53 is not a divisor of 2872)