What are the divisors of 3030?

1, 2, 3, 5, 6, 10, 15, 30, 101, 202, 303, 505, 606, 1010, 1515, 3030

There is a total of 16 positive divisors.
The sum of these divisors is 7344.
The arithmetic mean is 459.

8 even divisors

2, 6, 10, 30, 202, 606, 1010, 3030

8 odd divisors

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

How to compute the divisors of 3030?

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 3030 by each of the numbers from 1 to 3030 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)

3030 / 1 = 3030 (the remainder is 0, so 1 is a divisor of 3030)
3030 / 2 = 1515 (the remainder is 0, so 2 is a divisor of 3030)
3030 / 3 = 1010 (the remainder is 0, so 3 is a divisor of 3030)
...
3030 / 3029 = 1.000330141961 (the remainder is 1, so 3029 is not a divisor of 3030)
3030 / 3030 = 1 (the remainder is 0, so 3030 is a divisor of 3030)

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 3030 (i.e. 55.045435778092). 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 $\frac{N}{d} = D$ )

3030 / 1 = 3030 (the remainder is 0, so 1 and 3030 are divisors of 3030)
3030 / 2 = 1515 (the remainder is 0, so 2 and 1515 are divisors of 3030)
3030 / 3 = 1010 (the remainder is 0, so 3 and 1010 are divisors of 3030)
...
3030 / 54 = 56.111111111111 (the remainder is 6, so 54 is not a divisor of 3030)
3030 / 55 = 55.090909090909 (the remainder is 5, so 55 is not a divisor of 3030)