What are the divisors of 6027?

1, 3, 7, 21, 41, 49, 123, 147, 287, 861, 2009, 6027

There is a total of 12 positive divisors.
The sum of these divisors is 9576.
The arithmetic mean is 798.

12 odd divisors

1, 3, 7, 21, 41, 49, 123, 147, 287, 861, 2009, 6027

How to compute the divisors of 6027?

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 6027 by each of the numbers from 1 to 6027 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)

6027 / 1 = 6027 (the remainder is 0, so 1 is a divisor of 6027)
6027 / 2 = 3013.5 (the remainder is 1, so 2 is not a divisor of 6027)
6027 / 3 = 2009 (the remainder is 0, so 3 is a divisor of 6027)
...
6027 / 6026 = 1.0001659475606 (the remainder is 1, so 6026 is not a divisor of 6027)
6027 / 6027 = 1 (the remainder is 0, so 6027 is a divisor of 6027)

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 6027 (i.e. 77.633755544866). 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 $\frac{N}{d} = D$ )

6027 / 1 = 6027 (the remainder is 0, so 1 and 6027 are divisors of 6027)
6027 / 2 = 3013.5 (the remainder is 1, so 2 is not a divisor of 6027)
6027 / 3 = 2009 (the remainder is 0, so 3 and 2009 are divisors of 6027)
...
6027 / 76 = 79.302631578947 (the remainder is 23, so 76 is not a divisor of 6027)
6027 / 77 = 78.272727272727 (the remainder is 21, so 77 is not a divisor of 6027)