What are the divisors of 2746?

1, 2, 1373, 2746

There is a total of 4 positive divisors.
The sum of these divisors is 4122.
The arithmetic mean is 1030.5.

2 even divisors

2, 2746

2 odd divisors

1, 1373

How to compute the divisors of 2746?

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 2746 by each of the numbers from 1 to 2746 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)

2746 / 1 = 2746 (the remainder is 0, so 1 is a divisor of 2746)
2746 / 2 = 1373 (the remainder is 0, so 2 is a divisor of 2746)
2746 / 3 = 915.33333333333 (the remainder is 1, so 3 is not a divisor of 2746)
...
2746 / 2745 = 1.000364298725 (the remainder is 1, so 2745 is not a divisor of 2746)
2746 / 2746 = 1 (the remainder is 0, so 2746 is a divisor of 2746)

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 2746 (i.e. 52.402290026296). 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 $\frac{N}{d} = D$ )

2746 / 1 = 2746 (the remainder is 0, so 1 and 2746 are divisors of 2746)
2746 / 2 = 1373 (the remainder is 0, so 2 and 1373 are divisors of 2746)
2746 / 3 = 915.33333333333 (the remainder is 1, so 3 is not a divisor of 2746)
...
2746 / 51 = 53.843137254902 (the remainder is 43, so 51 is not a divisor of 2746)
2746 / 52 = 52.807692307692 (the remainder is 42, so 52 is not a divisor of 2746)