What are the divisors of 1738?

1, 2, 11, 22, 79, 158, 869, 1738

There is a total of 8 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 360.

4 even divisors

2, 22, 158, 1738

4 odd divisors

1, 11, 79, 869

How to compute the divisors of 1738?

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 1738 by each of the numbers from 1 to 1738 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)

1738 / 1 = 1738 (the remainder is 0, so 1 is a divisor of 1738)
1738 / 2 = 869 (the remainder is 0, so 2 is a divisor of 1738)
1738 / 3 = 579.33333333333 (the remainder is 1, so 3 is not a divisor of 1738)
...
1738 / 1737 = 1.0005757052389 (the remainder is 1, so 1737 is not a divisor of 1738)
1738 / 1738 = 1 (the remainder is 0, so 1738 is a divisor of 1738)

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 1738 (i.e. 41.689327171352). 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 $\frac{N}{d} = D$ )

1738 / 1 = 1738 (the remainder is 0, so 1 and 1738 are divisors of 1738)
1738 / 2 = 869 (the remainder is 0, so 2 and 869 are divisors of 1738)
1738 / 3 = 579.33333333333 (the remainder is 1, so 3 is not a divisor of 1738)
...
1738 / 40 = 43.45 (the remainder is 18, so 40 is not a divisor of 1738)
1738 / 41 = 42.390243902439 (the remainder is 16, so 41 is not a divisor of 1738)