What are the divisors of 6114?

1, 2, 3, 6, 1019, 2038, 3057, 6114

There is a total of 8 positive divisors.
The sum of these divisors is 12240.
The arithmetic mean is 1530.

4 even divisors

2, 6, 2038, 6114

4 odd divisors

1, 3, 1019, 3057

How to compute the divisors of 6114?

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 6114 by each of the numbers from 1 to 6114 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)

6114 / 1 = 6114 (the remainder is 0, so 1 is a divisor of 6114)
6114 / 2 = 3057 (the remainder is 0, so 2 is a divisor of 6114)
6114 / 3 = 2038 (the remainder is 0, so 3 is a divisor of 6114)
...
6114 / 6113 = 1.0001635858008 (the remainder is 1, so 6113 is not a divisor of 6114)
6114 / 6114 = 1 (the remainder is 0, so 6114 is a divisor of 6114)

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 6114 (i.e. 78.192071209298). 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 $\frac{N}{d} = D$ )

6114 / 1 = 6114 (the remainder is 0, so 1 and 6114 are divisors of 6114)
6114 / 2 = 3057 (the remainder is 0, so 2 and 3057 are divisors of 6114)
6114 / 3 = 2038 (the remainder is 0, so 3 and 2038 are divisors of 6114)
...
6114 / 77 = 79.402597402597 (the remainder is 31, so 77 is not a divisor of 6114)
6114 / 78 = 78.384615384615 (the remainder is 30, so 78 is not a divisor of 6114)