What are the divisors of 2846?

1, 2, 1423, 2846

There is a total of 4 positive divisors.
The sum of these divisors is 4272.
The arithmetic mean is 1068.

2 even divisors

2, 2846

2 odd divisors

1, 1423

How to compute the divisors of 2846?

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 2846 by each of the numbers from 1 to 2846 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)

2846 / 1 = 2846 (the remainder is 0, so 1 is a divisor of 2846)
2846 / 2 = 1423 (the remainder is 0, so 2 is a divisor of 2846)
2846 / 3 = 948.66666666667 (the remainder is 2, so 3 is not a divisor of 2846)
...
2846 / 2845 = 1.0003514938489 (the remainder is 1, so 2845 is not a divisor of 2846)
2846 / 2846 = 1 (the remainder is 0, so 2846 is a divisor of 2846)

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 2846 (i.e. 53.347914673397). 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 $\frac{N}{d} = D$ )

2846 / 1 = 2846 (the remainder is 0, so 1 and 2846 are divisors of 2846)
2846 / 2 = 1423 (the remainder is 0, so 2 and 1423 are divisors of 2846)
2846 / 3 = 948.66666666667 (the remainder is 2, so 3 is not a divisor of 2846)
...
2846 / 52 = 54.730769230769 (the remainder is 38, so 52 is not a divisor of 2846)
2846 / 53 = 53.698113207547 (the remainder is 37, so 53 is not a divisor of 2846)