What are the divisors of 1763?

1, 41, 43, 1763

There is a total of 4 positive divisors.
The sum of these divisors is 1848.
The arithmetic mean is 462.

4 odd divisors

1, 41, 43, 1763

How to compute the divisors of 1763?

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 1763 by each of the numbers from 1 to 1763 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)

1763 / 1 = 1763 (the remainder is 0, so 1 is a divisor of 1763)
1763 / 2 = 881.5 (the remainder is 1, so 2 is not a divisor of 1763)
1763 / 3 = 587.66666666667 (the remainder is 2, so 3 is not a divisor of 1763)
...
1763 / 1762 = 1.0005675368899 (the remainder is 1, so 1762 is not a divisor of 1763)
1763 / 1763 = 1 (the remainder is 0, so 1763 is a divisor of 1763)

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 1763 (i.e. 41.988093550434). 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 $\frac{N}{d} = D$ )

1763 / 1 = 1763 (the remainder is 0, so 1 and 1763 are divisors of 1763)
1763 / 2 = 881.5 (the remainder is 1, so 2 is not a divisor of 1763)
1763 / 3 = 587.66666666667 (the remainder is 2, so 3 is not a divisor of 1763)
...
1763 / 40 = 44.075 (the remainder is 3, so 40 is not a divisor of 1763)
1763 / 41 = 43 (the remainder is 0, so 41 and 43 are divisors of 1763)