What are the divisors of 2847?

1, 3, 13, 39, 73, 219, 949, 2847

There is a total of 8 positive divisors.
The sum of these divisors is 4144.
The arithmetic mean is 518.

8 odd divisors

1, 3, 13, 39, 73, 219, 949, 2847

How to compute the divisors of 2847?

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 2847 by each of the numbers from 1 to 2847 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)

2847 / 1 = 2847 (the remainder is 0, so 1 is a divisor of 2847)
2847 / 2 = 1423.5 (the remainder is 1, so 2 is not a divisor of 2847)
2847 / 3 = 949 (the remainder is 0, so 3 is a divisor of 2847)
...
2847 / 2846 = 1.0003513703443 (the remainder is 1, so 2846 is not a divisor of 2847)
2847 / 2847 = 1 (the remainder is 0, so 2847 is a divisor of 2847)

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 2847 (i.e. 53.357286287816). 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 $\frac{N}{d} = D$ )

2847 / 1 = 2847 (the remainder is 0, so 1 and 2847 are divisors of 2847)
2847 / 2 = 1423.5 (the remainder is 1, so 2 is not a divisor of 2847)
2847 / 3 = 949 (the remainder is 0, so 3 and 949 are divisors of 2847)
...
2847 / 52 = 54.75 (the remainder is 39, so 52 is not a divisor of 2847)
2847 / 53 = 53.716981132075 (the remainder is 38, so 53 is not a divisor of 2847)