What are the divisors of 3060?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 30, 34, 36, 45, 51, 60, 68, 85, 90, 102, 153, 170, 180, 204, 255, 306, 340, 510, 612, 765, 1020, 1530, 3060

There is a total of 36 positive divisors.
The sum of these divisors is 9828.
The arithmetic mean is 273.

24 even divisors

2, 4, 6, 10, 12, 18, 20, 30, 34, 36, 60, 68, 90, 102, 170, 180, 204, 306, 340, 510, 612, 1020, 1530, 3060

12 odd divisors

1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765

How to compute the divisors of 3060?

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 3060 by each of the numbers from 1 to 3060 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)

3060 / 1 = 3060 (the remainder is 0, so 1 is a divisor of 3060)
3060 / 2 = 1530 (the remainder is 0, so 2 is a divisor of 3060)
3060 / 3 = 1020 (the remainder is 0, so 3 is a divisor of 3060)
...
3060 / 3059 = 1.0003269042171 (the remainder is 1, so 3059 is not a divisor of 3060)
3060 / 3060 = 1 (the remainder is 0, so 3060 is a divisor of 3060)

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 3060 (i.e. 55.317266743757). 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 $\frac{N}{d} = D$ )

3060 / 1 = 3060 (the remainder is 0, so 1 and 3060 are divisors of 3060)
3060 / 2 = 1530 (the remainder is 0, so 2 and 1530 are divisors of 3060)
3060 / 3 = 1020 (the remainder is 0, so 3 and 1020 are divisors of 3060)
...
3060 / 54 = 56.666666666667 (the remainder is 36, so 54 is not a divisor of 3060)
3060 / 55 = 55.636363636364 (the remainder is 35, so 55 is not a divisor of 3060)