What are the divisors of 1730?

1, 2, 5, 10, 173, 346, 865, 1730

There is a total of 8 positive divisors.
The sum of these divisors is 3132.
The arithmetic mean is 391.5.

4 even divisors

2, 10, 346, 1730

4 odd divisors

1, 5, 173, 865

How to compute the divisors of 1730?

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 1730 by each of the numbers from 1 to 1730 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)

1730 / 1 = 1730 (the remainder is 0, so 1 is a divisor of 1730)
1730 / 2 = 865 (the remainder is 0, so 2 is a divisor of 1730)
1730 / 3 = 576.66666666667 (the remainder is 2, so 3 is not a divisor of 1730)
...
1730 / 1729 = 1.0005783689994 (the remainder is 1, so 1729 is not a divisor of 1730)
1730 / 1730 = 1 (the remainder is 0, so 1730 is a divisor of 1730)

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 1730 (i.e. 41.593268686171). 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 $\frac{N}{d} = D$ )

1730 / 1 = 1730 (the remainder is 0, so 1 and 1730 are divisors of 1730)
1730 / 2 = 865 (the remainder is 0, so 2 and 865 are divisors of 1730)
1730 / 3 = 576.66666666667 (the remainder is 2, so 3 is not a divisor of 1730)
...
1730 / 40 = 43.25 (the remainder is 10, so 40 is not a divisor of 1730)
1730 / 41 = 42.19512195122 (the remainder is 8, so 41 is not a divisor of 1730)