What are the divisors of 1736?

1, 2, 4, 7, 8, 14, 28, 31, 56, 62, 124, 217, 248, 434, 868, 1736

There is a total of 16 positive divisors.
The sum of these divisors is 3840.
The arithmetic mean is 240.

12 even divisors

2, 4, 8, 14, 28, 56, 62, 124, 248, 434, 868, 1736

4 odd divisors

1, 7, 31, 217

How to compute the divisors of 1736?

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 1736 by each of the numbers from 1 to 1736 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)

1736 / 1 = 1736 (the remainder is 0, so 1 is a divisor of 1736)
1736 / 2 = 868 (the remainder is 0, so 2 is a divisor of 1736)
1736 / 3 = 578.66666666667 (the remainder is 2, so 3 is not a divisor of 1736)
...
1736 / 1735 = 1.0005763688761 (the remainder is 1, so 1735 is not a divisor of 1736)
1736 / 1736 = 1 (the remainder is 0, so 1736 is a divisor of 1736)

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 1736 (i.e. 41.665333311999). 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 $\frac{N}{d} = D$ )

1736 / 1 = 1736 (the remainder is 0, so 1 and 1736 are divisors of 1736)
1736 / 2 = 868 (the remainder is 0, so 2 and 868 are divisors of 1736)
1736 / 3 = 578.66666666667 (the remainder is 2, so 3 is not a divisor of 1736)
...
1736 / 40 = 43.4 (the remainder is 16, so 40 is not a divisor of 1736)
1736 / 41 = 42.341463414634 (the remainder is 14, so 41 is not a divisor of 1736)