What are the divisors of 1750?

1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750

There is a total of 16 positive divisors.
The sum of these divisors is 3744.
The arithmetic mean is 234.

8 even divisors

2, 10, 14, 50, 70, 250, 350, 1750

8 odd divisors

1, 5, 7, 25, 35, 125, 175, 875

How to compute the divisors of 1750?

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 1750 by each of the numbers from 1 to 1750 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)

1750 / 1 = 1750 (the remainder is 0, so 1 is a divisor of 1750)
1750 / 2 = 875 (the remainder is 0, so 2 is a divisor of 1750)
1750 / 3 = 583.33333333333 (the remainder is 1, so 3 is not a divisor of 1750)
...
1750 / 1749 = 1.0005717552887 (the remainder is 1, so 1749 is not a divisor of 1750)
1750 / 1750 = 1 (the remainder is 0, so 1750 is a divisor of 1750)

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 1750 (i.e. 41.833001326704). 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 $\frac{N}{d} = D$ )

1750 / 1 = 1750 (the remainder is 0, so 1 and 1750 are divisors of 1750)
1750 / 2 = 875 (the remainder is 0, so 2 and 875 are divisors of 1750)
1750 / 3 = 583.33333333333 (the remainder is 1, so 3 is not a divisor of 1750)
...
1750 / 40 = 43.75 (the remainder is 30, so 40 is not a divisor of 1750)
1750 / 41 = 42.682926829268 (the remainder is 28, so 41 is not a divisor of 1750)