What are the divisors of 4067?

1, 7, 49, 83, 581, 4067

There is a total of 6 positive divisors.
The sum of these divisors is 4788.
The arithmetic mean is 798.

6 odd divisors

1, 7, 49, 83, 581, 4067

How to compute the divisors of 4067?

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 4067 by each of the numbers from 1 to 4067 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)

4067 / 1 = 4067 (the remainder is 0, so 1 is a divisor of 4067)
4067 / 2 = 2033.5 (the remainder is 1, so 2 is not a divisor of 4067)
4067 / 3 = 1355.6666666667 (the remainder is 2, so 3 is not a divisor of 4067)
...
4067 / 4066 = 1.0002459419577 (the remainder is 1, so 4066 is not a divisor of 4067)
4067 / 4067 = 1 (the remainder is 0, so 4067 is a divisor of 4067)

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 4067 (i.e. 63.77303505401). 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 $\frac{N}{d} = D$ )

4067 / 1 = 4067 (the remainder is 0, so 1 and 4067 are divisors of 4067)
4067 / 2 = 2033.5 (the remainder is 1, so 2 is not a divisor of 4067)
4067 / 3 = 1355.6666666667 (the remainder is 2, so 3 is not a divisor of 4067)
...
4067 / 62 = 65.596774193548 (the remainder is 37, so 62 is not a divisor of 4067)
4067 / 63 = 64.555555555556 (the remainder is 35, so 63 is not a divisor of 4067)