What are the divisors of 1766?

1, 2, 883, 1766

There is a total of 4 positive divisors.
The sum of these divisors is 2652.
The arithmetic mean is 663.

2 even divisors

2, 1766

2 odd divisors

1, 883

How to compute the divisors of 1766?

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 1766 by each of the numbers from 1 to 1766 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)

1766 / 1 = 1766 (the remainder is 0, so 1 is a divisor of 1766)
1766 / 2 = 883 (the remainder is 0, so 2 is a divisor of 1766)
1766 / 3 = 588.66666666667 (the remainder is 2, so 3 is not a divisor of 1766)
...
1766 / 1765 = 1.000566572238 (the remainder is 1, so 1765 is not a divisor of 1766)
1766 / 1766 = 1 (the remainder is 0, so 1766 is a divisor of 1766)

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 1766 (i.e. 42.023802778901). 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 $\frac{N}{d} = D$ )

1766 / 1 = 1766 (the remainder is 0, so 1 and 1766 are divisors of 1766)
1766 / 2 = 883 (the remainder is 0, so 2 and 883 are divisors of 1766)
1766 / 3 = 588.66666666667 (the remainder is 2, so 3 is not a divisor of 1766)
...
1766 / 41 = 43.073170731707 (the remainder is 3, so 41 is not a divisor of 1766)
1766 / 42 = 42.047619047619 (the remainder is 2, so 42 is not a divisor of 1766)