What are the divisors of 2817?

1, 3, 9, 313, 939, 2817

There is a total of 6 positive divisors.
The sum of these divisors is 4082.
The arithmetic mean is 680.33333333333.

6 odd divisors

1, 3, 9, 313, 939, 2817

How to compute the divisors of 2817?

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 2817 by each of the numbers from 1 to 2817 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)

2817 / 1 = 2817 (the remainder is 0, so 1 is a divisor of 2817)
2817 / 2 = 1408.5 (the remainder is 1, so 2 is not a divisor of 2817)
2817 / 3 = 939 (the remainder is 0, so 3 is a divisor of 2817)
...
2817 / 2816 = 1.0003551136364 (the remainder is 1, so 2816 is not a divisor of 2817)
2817 / 2817 = 1 (the remainder is 0, so 2817 is a divisor of 2817)

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 2817 (i.e. 53.075418038862). 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 $\frac{N}{d} = D$ )

2817 / 1 = 2817 (the remainder is 0, so 1 and 2817 are divisors of 2817)
2817 / 2 = 1408.5 (the remainder is 1, so 2 is not a divisor of 2817)
2817 / 3 = 939 (the remainder is 0, so 3 and 939 are divisors of 2817)
...
2817 / 52 = 54.173076923077 (the remainder is 9, so 52 is not a divisor of 2817)
2817 / 53 = 53.150943396226 (the remainder is 8, so 53 is not a divisor of 2817)