What are the divisors of 3785?

1, 5, 757, 3785

There is a total of 4 positive divisors.
The sum of these divisors is 4548.
The arithmetic mean is 1137.

4 odd divisors

1, 5, 757, 3785

How to compute the divisors of 3785?

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 3785 by each of the numbers from 1 to 3785 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)

3785 / 1 = 3785 (the remainder is 0, so 1 is a divisor of 3785)
3785 / 2 = 1892.5 (the remainder is 1, so 2 is not a divisor of 3785)
3785 / 3 = 1261.6666666667 (the remainder is 2, so 3 is not a divisor of 3785)
...
3785 / 3784 = 1.0002642706131 (the remainder is 1, so 3784 is not a divisor of 3785)
3785 / 3785 = 1 (the remainder is 0, so 3785 is a divisor of 3785)

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 3785 (i.e. 61.522353661088). 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 $\frac{N}{d} = D$ )

3785 / 1 = 3785 (the remainder is 0, so 1 and 3785 are divisors of 3785)
3785 / 2 = 1892.5 (the remainder is 1, so 2 is not a divisor of 3785)
3785 / 3 = 1261.6666666667 (the remainder is 2, so 3 is not a divisor of 3785)
...
3785 / 60 = 63.083333333333 (the remainder is 5, so 60 is not a divisor of 3785)
3785 / 61 = 62.049180327869 (the remainder is 3, so 61 is not a divisor of 3785)