What are the divisors of 2886?

1, 2, 3, 6, 13, 26, 37, 39, 74, 78, 111, 222, 481, 962, 1443, 2886

There is a total of 16 positive divisors.
The sum of these divisors is 6384.
The arithmetic mean is 399.

8 even divisors

2, 6, 26, 74, 78, 222, 962, 2886

8 odd divisors

1, 3, 13, 37, 39, 111, 481, 1443

How to compute the divisors of 2886?

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 2886 by each of the numbers from 1 to 2886 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)

2886 / 1 = 2886 (the remainder is 0, so 1 is a divisor of 2886)
2886 / 2 = 1443 (the remainder is 0, so 2 is a divisor of 2886)
2886 / 3 = 962 (the remainder is 0, so 3 is a divisor of 2886)
...
2886 / 2885 = 1.0003466204506 (the remainder is 1, so 2885 is not a divisor of 2886)
2886 / 2886 = 1 (the remainder is 0, so 2886 is a divisor of 2886)

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 2886 (i.e. 53.721504074253). 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 $\frac{N}{d} = D$ )

2886 / 1 = 2886 (the remainder is 0, so 1 and 2886 are divisors of 2886)
2886 / 2 = 1443 (the remainder is 0, so 2 and 1443 are divisors of 2886)
2886 / 3 = 962 (the remainder is 0, so 3 and 962 are divisors of 2886)
...
2886 / 52 = 55.5 (the remainder is 26, so 52 is not a divisor of 2886)
2886 / 53 = 54.452830188679 (the remainder is 24, so 53 is not a divisor of 2886)