What are the divisors of 6054?

1, 2, 3, 6, 1009, 2018, 3027, 6054

There is a total of 8 positive divisors.
The sum of these divisors is 12120.
The arithmetic mean is 1515.

4 even divisors

2, 6, 2018, 6054

4 odd divisors

1, 3, 1009, 3027

How to compute the divisors of 6054?

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 6054 by each of the numbers from 1 to 6054 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)

6054 / 1 = 6054 (the remainder is 0, so 1 is a divisor of 6054)
6054 / 2 = 3027 (the remainder is 0, so 2 is a divisor of 6054)
6054 / 3 = 2018 (the remainder is 0, so 3 is a divisor of 6054)
...
6054 / 6053 = 1.0001652073352 (the remainder is 1, so 6053 is not a divisor of 6054)
6054 / 6054 = 1 (the remainder is 0, so 6054 is a divisor of 6054)

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 6054 (i.e. 77.807454655708). 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 $\frac{N}{d} = D$ )

6054 / 1 = 6054 (the remainder is 0, so 1 and 6054 are divisors of 6054)
6054 / 2 = 3027 (the remainder is 0, so 2 and 3027 are divisors of 6054)
6054 / 3 = 2018 (the remainder is 0, so 3 and 2018 are divisors of 6054)
...
6054 / 76 = 79.657894736842 (the remainder is 50, so 76 is not a divisor of 6054)
6054 / 77 = 78.623376623377 (the remainder is 48, so 77 is not a divisor of 6054)