What are the divisors of 3067?

1, 3067

There is a total of 2 positive divisors.
The sum of these divisors is 3068.
The arithmetic mean is 1534.

2 odd divisors

1, 3067

How to compute the divisors of 3067?

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 3067 by each of the numbers from 1 to 3067 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)

3067 / 1 = 3067 (the remainder is 0, so 1 is a divisor of 3067)
3067 / 2 = 1533.5 (the remainder is 1, so 2 is not a divisor of 3067)
3067 / 3 = 1022.3333333333 (the remainder is 1, so 3 is not a divisor of 3067)
...
3067 / 3066 = 1.0003261578604 (the remainder is 1, so 3066 is not a divisor of 3067)
3067 / 3067 = 1 (the remainder is 0, so 3067 is a divisor of 3067)

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 3067 (i.e. 55.380501984002). 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 $\frac{N}{d} = D$ )

3067 / 1 = 3067 (the remainder is 0, so 1 and 3067 are divisors of 3067)
3067 / 2 = 1533.5 (the remainder is 1, so 2 is not a divisor of 3067)
3067 / 3 = 1022.3333333333 (the remainder is 1, so 3 is not a divisor of 3067)
...
3067 / 54 = 56.796296296296 (the remainder is 43, so 54 is not a divisor of 3067)
3067 / 55 = 55.763636363636 (the remainder is 42, so 55 is not a divisor of 3067)