What are the divisors of 1759?

1, 1759

There is a total of 2 positive divisors.
The sum of these divisors is 1760.
The arithmetic mean is 880.

2 odd divisors

1, 1759

How to compute the divisors of 1759?

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 1759 by each of the numbers from 1 to 1759 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)

1759 / 1 = 1759 (the remainder is 0, so 1 is a divisor of 1759)
1759 / 2 = 879.5 (the remainder is 1, so 2 is not a divisor of 1759)
1759 / 3 = 586.33333333333 (the remainder is 1, so 3 is not a divisor of 1759)
...
1759 / 1758 = 1.0005688282139 (the remainder is 1, so 1758 is not a divisor of 1759)
1759 / 1759 = 1 (the remainder is 0, so 1759 is a divisor of 1759)

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 1759 (i.e. 41.940433951022). 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 $\frac{N}{d} = D$ )

1759 / 1 = 1759 (the remainder is 0, so 1 and 1759 are divisors of 1759)
1759 / 2 = 879.5 (the remainder is 1, so 2 is not a divisor of 1759)
1759 / 3 = 586.33333333333 (the remainder is 1, so 3 is not a divisor of 1759)
...
1759 / 40 = 43.975 (the remainder is 39, so 40 is not a divisor of 1759)
1759 / 41 = 42.90243902439 (the remainder is 37, so 41 is not a divisor of 1759)