What are the divisors of 5067?

1, 3, 9, 563, 1689, 5067

There is a total of 6 positive divisors.
The sum of these divisors is 7332.
The arithmetic mean is 1222.

6 odd divisors

1, 3, 9, 563, 1689, 5067

How to compute the divisors of 5067?

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 5067 by each of the numbers from 1 to 5067 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)

5067 / 1 = 5067 (the remainder is 0, so 1 is a divisor of 5067)
5067 / 2 = 2533.5 (the remainder is 1, so 2 is not a divisor of 5067)
5067 / 3 = 1689 (the remainder is 0, so 3 is a divisor of 5067)
...
5067 / 5066 = 1.000197394394 (the remainder is 1, so 5066 is not a divisor of 5067)
5067 / 5067 = 1 (the remainder is 0, so 5067 is a divisor of 5067)

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 5067 (i.e. 71.182863106228). 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 $\frac{N}{d} = D$ )

5067 / 1 = 5067 (the remainder is 0, so 1 and 5067 are divisors of 5067)
5067 / 2 = 2533.5 (the remainder is 1, so 2 is not a divisor of 5067)
5067 / 3 = 1689 (the remainder is 0, so 3 and 1689 are divisors of 5067)
...
5067 / 70 = 72.385714285714 (the remainder is 27, so 70 is not a divisor of 5067)
5067 / 71 = 71.366197183099 (the remainder is 26, so 71 is not a divisor of 5067)