What are the divisors of 2860?

1, 2, 4, 5, 10, 11, 13, 20, 22, 26, 44, 52, 55, 65, 110, 130, 143, 220, 260, 286, 572, 715, 1430, 2860

There is a total of 24 positive divisors.
The sum of these divisors is 7056.
The arithmetic mean is 294.

16 even divisors

2, 4, 10, 20, 22, 26, 44, 52, 110, 130, 220, 260, 286, 572, 1430, 2860

8 odd divisors

1, 5, 11, 13, 55, 65, 143, 715

How to compute the divisors of 2860?

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 2860 by each of the numbers from 1 to 2860 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)

2860 / 1 = 2860 (the remainder is 0, so 1 is a divisor of 2860)
2860 / 2 = 1430 (the remainder is 0, so 2 is a divisor of 2860)
2860 / 3 = 953.33333333333 (the remainder is 1, so 3 is not a divisor of 2860)
...
2860 / 2859 = 1.0003497726478 (the remainder is 1, so 2859 is not a divisor of 2860)
2860 / 2860 = 1 (the remainder is 0, so 2860 is a divisor of 2860)

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 2860 (i.e. 53.478967828484). 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 $\frac{N}{d} = D$ )

2860 / 1 = 2860 (the remainder is 0, so 1 and 2860 are divisors of 2860)
2860 / 2 = 1430 (the remainder is 0, so 2 and 1430 are divisors of 2860)
2860 / 3 = 953.33333333333 (the remainder is 1, so 3 is not a divisor of 2860)
...
2860 / 52 = 55 (the remainder is 0, so 52 and 55 are divisors of 2860)
2860 / 53 = 53.962264150943 (the remainder is 51, so 53 is not a divisor of 2860)