What are the divisors of 1795?

1, 5, 359, 1795

There is a total of 4 positive divisors.
The sum of these divisors is 2160.
The arithmetic mean is 540.

4 odd divisors

1, 5, 359, 1795

How to compute the divisors of 1795?

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 1795 by each of the numbers from 1 to 1795 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)

1795 / 1 = 1795 (the remainder is 0, so 1 is a divisor of 1795)
1795 / 2 = 897.5 (the remainder is 1, so 2 is not a divisor of 1795)
1795 / 3 = 598.33333333333 (the remainder is 1, so 3 is not a divisor of 1795)
...
1795 / 1794 = 1.0005574136009 (the remainder is 1, so 1794 is not a divisor of 1795)
1795 / 1795 = 1 (the remainder is 0, so 1795 is a divisor of 1795)

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 1795 (i.e. 42.36744032863). 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 $\frac{N}{d} = D$ )

1795 / 1 = 1795 (the remainder is 0, so 1 and 1795 are divisors of 1795)
1795 / 2 = 897.5 (the remainder is 1, so 2 is not a divisor of 1795)
1795 / 3 = 598.33333333333 (the remainder is 1, so 3 is not a divisor of 1795)
...
1795 / 41 = 43.780487804878 (the remainder is 32, so 41 is not a divisor of 1795)
1795 / 42 = 42.738095238095 (the remainder is 31, so 42 is not a divisor of 1795)