What are the divisors of 2883?

1, 3, 31, 93, 961, 2883

There is a total of 6 positive divisors.
The sum of these divisors is 3972.
The arithmetic mean is 662.

6 odd divisors

1, 3, 31, 93, 961, 2883

How to compute the divisors of 2883?

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 2883 by each of the numbers from 1 to 2883 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)

2883 / 1 = 2883 (the remainder is 0, so 1 is a divisor of 2883)
2883 / 2 = 1441.5 (the remainder is 1, so 2 is not a divisor of 2883)
2883 / 3 = 961 (the remainder is 0, so 3 is a divisor of 2883)
...
2883 / 2882 = 1.000346981263 (the remainder is 1, so 2882 is not a divisor of 2883)
2883 / 2883 = 1 (the remainder is 0, so 2883 is a divisor of 2883)

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 2883 (i.e. 53.693575034635). 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 $\frac{N}{d} = D$ )

2883 / 1 = 2883 (the remainder is 0, so 1 and 2883 are divisors of 2883)
2883 / 2 = 1441.5 (the remainder is 1, so 2 is not a divisor of 2883)
2883 / 3 = 961 (the remainder is 0, so 3 and 961 are divisors of 2883)
...
2883 / 52 = 55.442307692308 (the remainder is 23, so 52 is not a divisor of 2883)
2883 / 53 = 54.396226415094 (the remainder is 21, so 53 is not a divisor of 2883)