What are the divisors of 1713?

1, 3, 571, 1713

There is a total of 4 positive divisors.
The sum of these divisors is 2288.
The arithmetic mean is 572.

4 odd divisors

1, 3, 571, 1713

How to compute the divisors of 1713?

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 1713 by each of the numbers from 1 to 1713 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)

1713 / 1 = 1713 (the remainder is 0, so 1 is a divisor of 1713)
1713 / 2 = 856.5 (the remainder is 1, so 2 is not a divisor of 1713)
1713 / 3 = 571 (the remainder is 0, so 3 is a divisor of 1713)
...
1713 / 1712 = 1.0005841121495 (the remainder is 1, so 1712 is not a divisor of 1713)
1713 / 1713 = 1 (the remainder is 0, so 1713 is a divisor of 1713)

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 1713 (i.e. 41.38840417315). 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 $\frac{N}{d} = D$ )

1713 / 1 = 1713 (the remainder is 0, so 1 and 1713 are divisors of 1713)
1713 / 2 = 856.5 (the remainder is 1, so 2 is not a divisor of 1713)
1713 / 3 = 571 (the remainder is 0, so 3 and 571 are divisors of 1713)
...
1713 / 40 = 42.825 (the remainder is 33, so 40 is not a divisor of 1713)
1713 / 41 = 41.780487804878 (the remainder is 32, so 41 is not a divisor of 1713)