What are the divisors of 1765?

1, 5, 353, 1765

There is a total of 4 positive divisors.
The sum of these divisors is 2124.
The arithmetic mean is 531.

4 odd divisors

1, 5, 353, 1765

How to compute the divisors of 1765?

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 1765 by each of the numbers from 1 to 1765 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)

1765 / 1 = 1765 (the remainder is 0, so 1 is a divisor of 1765)
1765 / 2 = 882.5 (the remainder is 1, so 2 is not a divisor of 1765)
1765 / 3 = 588.33333333333 (the remainder is 1, so 3 is not a divisor of 1765)
...
1765 / 1764 = 1.000566893424 (the remainder is 1, so 1764 is not a divisor of 1765)
1765 / 1765 = 1 (the remainder is 0, so 1765 is a divisor of 1765)

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 1765 (i.e. 42.0119030752). 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 $\frac{N}{d} = D$ )

1765 / 1 = 1765 (the remainder is 0, so 1 and 1765 are divisors of 1765)
1765 / 2 = 882.5 (the remainder is 1, so 2 is not a divisor of 1765)
1765 / 3 = 588.33333333333 (the remainder is 1, so 3 is not a divisor of 1765)
...
1765 / 41 = 43.048780487805 (the remainder is 2, so 41 is not a divisor of 1765)
1765 / 42 = 42.02380952381 (the remainder is 1, so 42 is not a divisor of 1765)