What are the divisors of 2742?

1, 2, 3, 6, 457, 914, 1371, 2742

There is a total of 8 positive divisors.
The sum of these divisors is 5496.
The arithmetic mean is 687.

4 even divisors

2, 6, 914, 2742

4 odd divisors

1, 3, 457, 1371

How to compute the divisors of 2742?

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 2742 by each of the numbers from 1 to 2742 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)

2742 / 1 = 2742 (the remainder is 0, so 1 is a divisor of 2742)
2742 / 2 = 1371 (the remainder is 0, so 2 is a divisor of 2742)
2742 / 3 = 914 (the remainder is 0, so 3 is a divisor of 2742)
...
2742 / 2741 = 1.0003648303539 (the remainder is 1, so 2741 is not a divisor of 2742)
2742 / 2742 = 1 (the remainder is 0, so 2742 is a divisor of 2742)

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 2742 (i.e. 52.364109846344). 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 $\frac{N}{d} = D$ )

2742 / 1 = 2742 (the remainder is 0, so 1 and 2742 are divisors of 2742)
2742 / 2 = 1371 (the remainder is 0, so 2 and 1371 are divisors of 2742)
2742 / 3 = 914 (the remainder is 0, so 3 and 914 are divisors of 2742)
...
2742 / 51 = 53.764705882353 (the remainder is 39, so 51 is not a divisor of 2742)
2742 / 52 = 52.730769230769 (the remainder is 38, so 52 is not a divisor of 2742)