What are the divisors of 1708?

1, 2, 4, 7, 14, 28, 61, 122, 244, 427, 854, 1708

There is a total of 12 positive divisors.
The sum of these divisors is 3472.
The arithmetic mean is 289.33333333333.

8 even divisors

2, 4, 14, 28, 122, 244, 854, 1708

4 odd divisors

1, 7, 61, 427

How to compute the divisors of 1708?

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 1708 by each of the numbers from 1 to 1708 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)

1708 / 1 = 1708 (the remainder is 0, so 1 is a divisor of 1708)
1708 / 2 = 854 (the remainder is 0, so 2 is a divisor of 1708)
1708 / 3 = 569.33333333333 (the remainder is 1, so 3 is not a divisor of 1708)
...
1708 / 1707 = 1.0005858230814 (the remainder is 1, so 1707 is not a divisor of 1708)
1708 / 1708 = 1 (the remainder is 0, so 1708 is a divisor of 1708)

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 1708 (i.e. 41.327956639544). 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 $\frac{N}{d} = D$ )

1708 / 1 = 1708 (the remainder is 0, so 1 and 1708 are divisors of 1708)
1708 / 2 = 854 (the remainder is 0, so 2 and 854 are divisors of 1708)
1708 / 3 = 569.33333333333 (the remainder is 1, so 3 is not a divisor of 1708)
...
1708 / 40 = 42.7 (the remainder is 28, so 40 is not a divisor of 1708)
1708 / 41 = 41.658536585366 (the remainder is 27, so 41 is not a divisor of 1708)