What are the divisors of 6090?

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 29, 30, 35, 42, 58, 70, 87, 105, 145, 174, 203, 210, 290, 406, 435, 609, 870, 1015, 1218, 2030, 3045, 6090

There is a total of 32 positive divisors.
The sum of these divisors is 17280.
The arithmetic mean is 540.

16 even divisors

2, 6, 10, 14, 30, 42, 58, 70, 174, 210, 290, 406, 870, 1218, 2030, 6090

16 odd divisors

1, 3, 5, 7, 15, 21, 29, 35, 87, 105, 145, 203, 435, 609, 1015, 3045

How to compute the divisors of 6090?

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 6090 by each of the numbers from 1 to 6090 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)

6090 / 1 = 6090 (the remainder is 0, so 1 is a divisor of 6090)
6090 / 2 = 3045 (the remainder is 0, so 2 is a divisor of 6090)
6090 / 3 = 2030 (the remainder is 0, so 3 is a divisor of 6090)
...
6090 / 6089 = 1.0001642305797 (the remainder is 1, so 6089 is not a divisor of 6090)
6090 / 6090 = 1 (the remainder is 0, so 6090 is a divisor of 6090)

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 6090 (i.e. 78.038452060507). 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 $\frac{N}{d} = D$ )

6090 / 1 = 6090 (the remainder is 0, so 1 and 6090 are divisors of 6090)
6090 / 2 = 3045 (the remainder is 0, so 2 and 3045 are divisors of 6090)
6090 / 3 = 2030 (the remainder is 0, so 3 and 2030 are divisors of 6090)
...
6090 / 77 = 79.090909090909 (the remainder is 7, so 77 is not a divisor of 6090)
6090 / 78 = 78.076923076923 (the remainder is 6, so 78 is not a divisor of 6090)