What are the divisors of 2696?

1, 2, 4, 8, 337, 674, 1348, 2696

There is a total of 8 positive divisors.
The sum of these divisors is 5070.
The arithmetic mean is 633.75.

6 even divisors

2, 4, 8, 674, 1348, 2696

2 odd divisors

1, 337

How to compute the divisors of 2696?

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 2696 by each of the numbers from 1 to 2696 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)

2696 / 1 = 2696 (the remainder is 0, so 1 is a divisor of 2696)
2696 / 2 = 1348 (the remainder is 0, so 2 is a divisor of 2696)
2696 / 3 = 898.66666666667 (the remainder is 2, so 3 is not a divisor of 2696)
...
2696 / 2695 = 1.0003710575139 (the remainder is 1, so 2695 is not a divisor of 2696)
2696 / 2696 = 1 (the remainder is 0, so 2696 is a divisor of 2696)

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 2696 (i.e. 51.923019942989). 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 $\frac{N}{d} = D$ )

2696 / 1 = 2696 (the remainder is 0, so 1 and 2696 are divisors of 2696)
2696 / 2 = 1348 (the remainder is 0, so 2 and 1348 are divisors of 2696)
2696 / 3 = 898.66666666667 (the remainder is 2, so 3 is not a divisor of 2696)
...
2696 / 50 = 53.92 (the remainder is 46, so 50 is not a divisor of 2696)
2696 / 51 = 52.862745098039 (the remainder is 44, so 51 is not a divisor of 2696)