What are the divisors of 6111?

1, 3, 7, 9, 21, 63, 97, 291, 679, 873, 2037, 6111

There is a total of 12 positive divisors.
The sum of these divisors is 10192.
The arithmetic mean is 849.33333333333.

12 odd divisors

1, 3, 7, 9, 21, 63, 97, 291, 679, 873, 2037, 6111

How to compute the divisors of 6111?

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 6111 by each of the numbers from 1 to 6111 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)

6111 / 1 = 6111 (the remainder is 0, so 1 is a divisor of 6111)
6111 / 2 = 3055.5 (the remainder is 1, so 2 is not a divisor of 6111)
6111 / 3 = 2037 (the remainder is 0, so 3 is a divisor of 6111)
...
6111 / 6110 = 1.0001636661211 (the remainder is 1, so 6110 is not a divisor of 6111)
6111 / 6111 = 1 (the remainder is 0, so 6111 is a divisor of 6111)

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 6111 (i.e. 78.172885324772). 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 $\frac{N}{d} = D$ )

6111 / 1 = 6111 (the remainder is 0, so 1 and 6111 are divisors of 6111)
6111 / 2 = 3055.5 (the remainder is 1, so 2 is not a divisor of 6111)
6111 / 3 = 2037 (the remainder is 0, so 3 and 2037 are divisors of 6111)
...
6111 / 77 = 79.363636363636 (the remainder is 28, so 77 is not a divisor of 6111)
6111 / 78 = 78.346153846154 (the remainder is 27, so 78 is not a divisor of 6111)