What are the divisors of 2713?

1, 2713

There is a total of 2 positive divisors.
The sum of these divisors is 2714.
The arithmetic mean is 1357.

2 odd divisors

1, 2713

How to compute the divisors of 2713?

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 2713 by each of the numbers from 1 to 2713 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)

2713 / 1 = 2713 (the remainder is 0, so 1 is a divisor of 2713)
2713 / 2 = 1356.5 (the remainder is 1, so 2 is not a divisor of 2713)
2713 / 3 = 904.33333333333 (the remainder is 1, so 3 is not a divisor of 2713)
...
2713 / 2712 = 1.0003687315634 (the remainder is 1, so 2712 is not a divisor of 2713)
2713 / 2713 = 1 (the remainder is 0, so 2713 is a divisor of 2713)

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 2713 (i.e. 52.086466572422). 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 $\frac{N}{d} = D$ )

2713 / 1 = 2713 (the remainder is 0, so 1 and 2713 are divisors of 2713)
2713 / 2 = 1356.5 (the remainder is 1, so 2 is not a divisor of 2713)
2713 / 3 = 904.33333333333 (the remainder is 1, so 3 is not a divisor of 2713)
...
2713 / 51 = 53.196078431373 (the remainder is 10, so 51 is not a divisor of 2713)
2713 / 52 = 52.173076923077 (the remainder is 9, so 52 is not a divisor of 2713)