What are the divisors of 1756?

1, 2, 4, 439, 878, 1756

There is a total of 6 positive divisors.
The sum of these divisors is 3080.
The arithmetic mean is 513.33333333333.

4 even divisors

2, 4, 878, 1756

2 odd divisors

1, 439

How to compute the divisors of 1756?

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 1756 by each of the numbers from 1 to 1756 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)

1756 / 1 = 1756 (the remainder is 0, so 1 is a divisor of 1756)
1756 / 2 = 878 (the remainder is 0, so 2 is a divisor of 1756)
1756 / 3 = 585.33333333333 (the remainder is 1, so 3 is not a divisor of 1756)
...
1756 / 1755 = 1.0005698005698 (the remainder is 1, so 1755 is not a divisor of 1756)
1756 / 1756 = 1 (the remainder is 0, so 1756 is a divisor of 1756)

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 1756 (i.e. 41.904653679514). 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 $\frac{N}{d} = D$ )

1756 / 1 = 1756 (the remainder is 0, so 1 and 1756 are divisors of 1756)
1756 / 2 = 878 (the remainder is 0, so 2 and 878 are divisors of 1756)
1756 / 3 = 585.33333333333 (the remainder is 1, so 3 is not a divisor of 1756)
...
1756 / 40 = 43.9 (the remainder is 36, so 40 is not a divisor of 1756)
1756 / 41 = 42.829268292683 (the remainder is 34, so 41 is not a divisor of 1756)