What are the divisors of 3065?

1, 5, 613, 3065

There is a total of 4 positive divisors.
The sum of these divisors is 3684.
The arithmetic mean is 921.

4 odd divisors

1, 5, 613, 3065

How to compute the divisors of 3065?

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 3065 by each of the numbers from 1 to 3065 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)

3065 / 1 = 3065 (the remainder is 0, so 1 is a divisor of 3065)
3065 / 2 = 1532.5 (the remainder is 1, so 2 is not a divisor of 3065)
3065 / 3 = 1021.6666666667 (the remainder is 2, so 3 is not a divisor of 3065)
...
3065 / 3064 = 1.0003263707572 (the remainder is 1, so 3064 is not a divisor of 3065)
3065 / 3065 = 1 (the remainder is 0, so 3065 is a divisor of 3065)

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 3065 (i.e. 55.362442142666). 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 $\frac{N}{d} = D$ )

3065 / 1 = 3065 (the remainder is 0, so 1 and 3065 are divisors of 3065)
3065 / 2 = 1532.5 (the remainder is 1, so 2 is not a divisor of 3065)
3065 / 3 = 1021.6666666667 (the remainder is 2, so 3 is not a divisor of 3065)
...
3065 / 54 = 56.759259259259 (the remainder is 41, so 54 is not a divisor of 3065)
3065 / 55 = 55.727272727273 (the remainder is 40, so 55 is not a divisor of 3065)