What are the divisors of 696?

1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, 696

There is a total of 16 positive divisors.
The sum of these divisors is 1800.
The arithmetic mean is 112.5.

12 even divisors

2, 4, 6, 8, 12, 24, 58, 116, 174, 232, 348, 696

4 odd divisors

1, 3, 29, 87

How to compute the divisors of 696?

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 696 by each of the numbers from 1 to 696 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)

696 / 1 = 696 (the remainder is 0, so 1 is a divisor of 696)
696 / 2 = 348 (the remainder is 0, so 2 is a divisor of 696)
696 / 3 = 232 (the remainder is 0, so 3 is a divisor of 696)
...
696 / 695 = 1.0014388489209 (the remainder is 1, so 695 is not a divisor of 696)
696 / 696 = 1 (the remainder is 0, so 696 is a divisor of 696)

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 696 (i.e. 26.381811916546). 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 $\frac{N}{d} = D$ )

696 / 1 = 696 (the remainder is 0, so 1 and 696 are divisors of 696)
696 / 2 = 348 (the remainder is 0, so 2 and 348 are divisors of 696)
696 / 3 = 232 (the remainder is 0, so 3 and 232 are divisors of 696)
...
696 / 25 = 27.84 (the remainder is 21, so 25 is not a divisor of 696)
696 / 26 = 26.769230769231 (the remainder is 20, so 26 is not a divisor of 696)