What are the divisors of 1707?

1, 3, 569, 1707

There is a total of 4 positive divisors.
The sum of these divisors is 2280.
The arithmetic mean is 570.

4 odd divisors

1, 3, 569, 1707

How to compute the divisors of 1707?

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 1707 by each of the numbers from 1 to 1707 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)

1707 / 1 = 1707 (the remainder is 0, so 1 is a divisor of 1707)
1707 / 2 = 853.5 (the remainder is 1, so 2 is not a divisor of 1707)
1707 / 3 = 569 (the remainder is 0, so 3 is a divisor of 1707)
...
1707 / 1706 = 1.0005861664713 (the remainder is 1, so 1706 is not a divisor of 1707)
1707 / 1707 = 1 (the remainder is 0, so 1707 is a divisor of 1707)

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 1707 (i.e. 41.315856520227). 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 $\frac{N}{d} = D$ )

1707 / 1 = 1707 (the remainder is 0, so 1 and 1707 are divisors of 1707)
1707 / 2 = 853.5 (the remainder is 1, so 2 is not a divisor of 1707)
1707 / 3 = 569 (the remainder is 0, so 3 and 569 are divisors of 1707)
...
1707 / 40 = 42.675 (the remainder is 27, so 40 is not a divisor of 1707)
1707 / 41 = 41.634146341463 (the remainder is 26, so 41 is not a divisor of 1707)