What are the divisors of 1717?

1, 17, 101, 1717

There is a total of 4 positive divisors.
The sum of these divisors is 1836.
The arithmetic mean is 459.

4 odd divisors

1, 17, 101, 1717

How to compute the divisors of 1717?

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 1717 by each of the numbers from 1 to 1717 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)

1717 / 1 = 1717 (the remainder is 0, so 1 is a divisor of 1717)
1717 / 2 = 858.5 (the remainder is 1, so 2 is not a divisor of 1717)
1717 / 3 = 572.33333333333 (the remainder is 1, so 3 is not a divisor of 1717)
...
1717 / 1716 = 1.0005827505828 (the remainder is 1, so 1716 is not a divisor of 1717)
1717 / 1717 = 1 (the remainder is 0, so 1717 is a divisor of 1717)

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 1717 (i.e. 41.436698710201). 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 $\frac{N}{d} = D$ )

1717 / 1 = 1717 (the remainder is 0, so 1 and 1717 are divisors of 1717)
1717 / 2 = 858.5 (the remainder is 1, so 2 is not a divisor of 1717)
1717 / 3 = 572.33333333333 (the remainder is 1, so 3 is not a divisor of 1717)
...
1717 / 40 = 42.925 (the remainder is 37, so 40 is not a divisor of 1717)
1717 / 41 = 41.878048780488 (the remainder is 36, so 41 is not a divisor of 1717)