What are the divisors of 2714?

1, 2, 23, 46, 59, 118, 1357, 2714

There is a total of 8 positive divisors.
The sum of these divisors is 4320.
The arithmetic mean is 540.

4 even divisors

2, 46, 118, 2714

4 odd divisors

1, 23, 59, 1357

How to compute the divisors of 2714?

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 2714 by each of the numbers from 1 to 2714 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)

2714 / 1 = 2714 (the remainder is 0, so 1 is a divisor of 2714)
2714 / 2 = 1357 (the remainder is 0, so 2 is a divisor of 2714)
2714 / 3 = 904.66666666667 (the remainder is 2, so 3 is not a divisor of 2714)
...
2714 / 2713 = 1.0003685956506 (the remainder is 1, so 2713 is not a divisor of 2714)
2714 / 2714 = 1 (the remainder is 0, so 2714 is a divisor of 2714)

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 2714 (i.e. 52.096065110524). 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 $\frac{N}{d} = D$ )

2714 / 1 = 2714 (the remainder is 0, so 1 and 2714 are divisors of 2714)
2714 / 2 = 1357 (the remainder is 0, so 2 and 1357 are divisors of 2714)
2714 / 3 = 904.66666666667 (the remainder is 2, so 3 is not a divisor of 2714)
...
2714 / 51 = 53.21568627451 (the remainder is 11, so 51 is not a divisor of 2714)
2714 / 52 = 52.192307692308 (the remainder is 10, so 52 is not a divisor of 2714)