What are the divisors of 3510?

1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 27, 30, 39, 45, 54, 65, 78, 90, 117, 130, 135, 195, 234, 270, 351, 390, 585, 702, 1170, 1755, 3510

There is a total of 32 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 315.

16 even divisors

2, 6, 10, 18, 26, 30, 54, 78, 90, 130, 234, 270, 390, 702, 1170, 3510

16 odd divisors

1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755

How to compute the divisors of 3510?

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 3510 by each of the numbers from 1 to 3510 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)

3510 / 1 = 3510 (the remainder is 0, so 1 is a divisor of 3510)
3510 / 2 = 1755 (the remainder is 0, so 2 is a divisor of 3510)
3510 / 3 = 1170 (the remainder is 0, so 3 is a divisor of 3510)
...
3510 / 3509 = 1.0002849814762 (the remainder is 1, so 3509 is not a divisor of 3510)
3510 / 3510 = 1 (the remainder is 0, so 3510 is a divisor of 3510)

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 3510 (i.e. 59.245252974394). 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 $\frac{N}{d} = D$ )

3510 / 1 = 3510 (the remainder is 0, so 1 and 3510 are divisors of 3510)
3510 / 2 = 1755 (the remainder is 0, so 2 and 1755 are divisors of 3510)
3510 / 3 = 1170 (the remainder is 0, so 3 and 1170 are divisors of 3510)
...
3510 / 58 = 60.51724137931 (the remainder is 30, so 58 is not a divisor of 3510)
3510 / 59 = 59.491525423729 (the remainder is 29, so 59 is not a divisor of 3510)