What are the divisors of 6069?

1, 3, 7, 17, 21, 51, 119, 289, 357, 867, 2023, 6069

There is a total of 12 positive divisors.
The sum of these divisors is 9824.
The arithmetic mean is 818.66666666667.

12 odd divisors

1, 3, 7, 17, 21, 51, 119, 289, 357, 867, 2023, 6069

How to compute the divisors of 6069?

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 6069 by each of the numbers from 1 to 6069 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)

6069 / 1 = 6069 (the remainder is 0, so 1 is a divisor of 6069)
6069 / 2 = 3034.5 (the remainder is 1, so 2 is not a divisor of 6069)
6069 / 3 = 2023 (the remainder is 0, so 3 is a divisor of 6069)
...
6069 / 6068 = 1.0001647989453 (the remainder is 1, so 6068 is not a divisor of 6069)
6069 / 6069 = 1 (the remainder is 0, so 6069 is a divisor of 6069)

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 6069 (i.e. 77.903786814249). 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 $\frac{N}{d} = D$ )

6069 / 1 = 6069 (the remainder is 0, so 1 and 6069 are divisors of 6069)
6069 / 2 = 3034.5 (the remainder is 1, so 2 is not a divisor of 6069)
6069 / 3 = 2023 (the remainder is 0, so 3 and 2023 are divisors of 6069)
...
6069 / 76 = 79.855263157895 (the remainder is 65, so 76 is not a divisor of 6069)
6069 / 77 = 78.818181818182 (the remainder is 63, so 77 is not a divisor of 6069)