What are the divisors of 1768?

1, 2, 4, 8, 13, 17, 26, 34, 52, 68, 104, 136, 221, 442, 884, 1768

There is a total of 16 positive divisors.
The sum of these divisors is 3780.
The arithmetic mean is 236.25.

12 even divisors

2, 4, 8, 26, 34, 52, 68, 104, 136, 442, 884, 1768

4 odd divisors

1, 13, 17, 221

How to compute the divisors of 1768?

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 1768 by each of the numbers from 1 to 1768 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)

1768 / 1 = 1768 (the remainder is 0, so 1 is a divisor of 1768)
1768 / 2 = 884 (the remainder is 0, so 2 is a divisor of 1768)
1768 / 3 = 589.33333333333 (the remainder is 1, so 3 is not a divisor of 1768)
...
1768 / 1767 = 1.0005659309564 (the remainder is 1, so 1767 is not a divisor of 1768)
1768 / 1768 = 1 (the remainder is 0, so 1768 is a divisor of 1768)

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 1768 (i.e. 42.047592083257). 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 $\frac{N}{d} = D$ )

1768 / 1 = 1768 (the remainder is 0, so 1 and 1768 are divisors of 1768)
1768 / 2 = 884 (the remainder is 0, so 2 and 884 are divisors of 1768)
1768 / 3 = 589.33333333333 (the remainder is 1, so 3 is not a divisor of 1768)
...
1768 / 41 = 43.121951219512 (the remainder is 5, so 41 is not a divisor of 1768)
1768 / 42 = 42.095238095238 (the remainder is 4, so 42 is not a divisor of 1768)