What are the divisors of 2743?

1, 13, 211, 2743

There is a total of 4 positive divisors.
The sum of these divisors is 2968.
The arithmetic mean is 742.

4 odd divisors

1, 13, 211, 2743

How to compute the divisors of 2743?

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 2743 by each of the numbers from 1 to 2743 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)

2743 / 1 = 2743 (the remainder is 0, so 1 is a divisor of 2743)
2743 / 2 = 1371.5 (the remainder is 1, so 2 is not a divisor of 2743)
2743 / 3 = 914.33333333333 (the remainder is 1, so 3 is not a divisor of 2743)
...
2743 / 2742 = 1.0003646973012 (the remainder is 1, so 2742 is not a divisor of 2743)
2743 / 2743 = 1 (the remainder is 0, so 2743 is a divisor of 2743)

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 2743 (i.e. 52.373657500694). 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 $\frac{N}{d} = D$ )

2743 / 1 = 2743 (the remainder is 0, so 1 and 2743 are divisors of 2743)
2743 / 2 = 1371.5 (the remainder is 1, so 2 is not a divisor of 2743)
2743 / 3 = 914.33333333333 (the remainder is 1, so 3 is not a divisor of 2743)
...
2743 / 51 = 53.78431372549 (the remainder is 40, so 51 is not a divisor of 2743)
2743 / 52 = 52.75 (the remainder is 39, so 52 is not a divisor of 2743)