What are the divisors of 1761?

1, 3, 587, 1761

There is a total of 4 positive divisors.
The sum of these divisors is 2352.
The arithmetic mean is 588.

4 odd divisors

1, 3, 587, 1761

How to compute the divisors of 1761?

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 1761 by each of the numbers from 1 to 1761 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)

1761 / 1 = 1761 (the remainder is 0, so 1 is a divisor of 1761)
1761 / 2 = 880.5 (the remainder is 1, so 2 is not a divisor of 1761)
1761 / 3 = 587 (the remainder is 0, so 3 is a divisor of 1761)
...
1761 / 1760 = 1.0005681818182 (the remainder is 1, so 1760 is not a divisor of 1761)
1761 / 1761 = 1 (the remainder is 0, so 1761 is a divisor of 1761)

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 1761 (i.e. 41.964270516715). 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 $\frac{N}{d} = D$ )

1761 / 1 = 1761 (the remainder is 0, so 1 and 1761 are divisors of 1761)
1761 / 2 = 880.5 (the remainder is 1, so 2 is not a divisor of 1761)
1761 / 3 = 587 (the remainder is 0, so 3 and 587 are divisors of 1761)
...
1761 / 40 = 44.025 (the remainder is 1, so 40 is not a divisor of 1761)
1761 / 41 = 42.951219512195 (the remainder is 39, so 41 is not a divisor of 1761)