What are the divisors of 2716?

1, 2, 4, 7, 14, 28, 97, 194, 388, 679, 1358, 2716

There is a total of 12 positive divisors.
The sum of these divisors is 5488.
The arithmetic mean is 457.33333333333.

8 even divisors

2, 4, 14, 28, 194, 388, 1358, 2716

4 odd divisors

1, 7, 97, 679

How to compute the divisors of 2716?

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 2716 by each of the numbers from 1 to 2716 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)

2716 / 1 = 2716 (the remainder is 0, so 1 is a divisor of 2716)
2716 / 2 = 1358 (the remainder is 0, so 2 is a divisor of 2716)
2716 / 3 = 905.33333333333 (the remainder is 1, so 3 is not a divisor of 2716)
...
2716 / 2715 = 1.0003683241252 (the remainder is 1, so 2715 is not a divisor of 2716)
2716 / 2716 = 1 (the remainder is 0, so 2716 is a divisor of 2716)

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 2716 (i.e. 52.115256883182). 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 $\frac{N}{d} = D$ )

2716 / 1 = 2716 (the remainder is 0, so 1 and 2716 are divisors of 2716)
2716 / 2 = 1358 (the remainder is 0, so 2 and 1358 are divisors of 2716)
2716 / 3 = 905.33333333333 (the remainder is 1, so 3 is not a divisor of 2716)
...
2716 / 51 = 53.254901960784 (the remainder is 13, so 51 is not a divisor of 2716)
2716 / 52 = 52.230769230769 (the remainder is 12, so 52 is not a divisor of 2716)