What are the divisors of 2747?

1, 41, 67, 2747

There is a total of 4 positive divisors.
The sum of these divisors is 2856.
The arithmetic mean is 714.

4 odd divisors

1, 41, 67, 2747

How to compute the divisors of 2747?

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 2747 by each of the numbers from 1 to 2747 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)

2747 / 1 = 2747 (the remainder is 0, so 1 is a divisor of 2747)
2747 / 2 = 1373.5 (the remainder is 1, so 2 is not a divisor of 2747)
2747 / 3 = 915.66666666667 (the remainder is 2, so 3 is not a divisor of 2747)
...
2747 / 2746 = 1.0003641660597 (the remainder is 1, so 2746 is not a divisor of 2747)
2747 / 2747 = 1 (the remainder is 0, so 2747 is a divisor of 2747)

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 2747 (i.e. 52.411830725515). 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 $\frac{N}{d} = D$ )

2747 / 1 = 2747 (the remainder is 0, so 1 and 2747 are divisors of 2747)
2747 / 2 = 1373.5 (the remainder is 1, so 2 is not a divisor of 2747)
2747 / 3 = 915.66666666667 (the remainder is 2, so 3 is not a divisor of 2747)
...
2747 / 51 = 53.862745098039 (the remainder is 44, so 51 is not a divisor of 2747)
2747 / 52 = 52.826923076923 (the remainder is 43, so 52 is not a divisor of 2747)