What are the divisors of 6060?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 101, 202, 303, 404, 505, 606, 1010, 1212, 1515, 2020, 3030, 6060

There is a total of 24 positive divisors.
The sum of these divisors is 17136.
The arithmetic mean is 714.

16 even divisors

2, 4, 6, 10, 12, 20, 30, 60, 202, 404, 606, 1010, 1212, 2020, 3030, 6060

8 odd divisors

1, 3, 5, 15, 101, 303, 505, 1515

How to compute the divisors of 6060?

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 6060 by each of the numbers from 1 to 6060 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)

6060 / 1 = 6060 (the remainder is 0, so 1 is a divisor of 6060)
6060 / 2 = 3030 (the remainder is 0, so 2 is a divisor of 6060)
6060 / 3 = 2020 (the remainder is 0, so 3 is a divisor of 6060)
...
6060 / 6059 = 1.0001650437366 (the remainder is 1, so 6059 is not a divisor of 6060)
6060 / 6060 = 1 (the remainder is 0, so 6060 is a divisor of 6060)

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 6060 (i.e. 77.846001824114). 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 $\frac{N}{d} = D$ )

6060 / 1 = 6060 (the remainder is 0, so 1 and 6060 are divisors of 6060)
6060 / 2 = 3030 (the remainder is 0, so 2 and 3030 are divisors of 6060)
6060 / 3 = 2020 (the remainder is 0, so 3 and 2020 are divisors of 6060)
...
6060 / 76 = 79.736842105263 (the remainder is 56, so 76 is not a divisor of 6060)
6060 / 77 = 78.701298701299 (the remainder is 54, so 77 is not a divisor of 6060)