What are the divisors of 3180?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 53, 60, 106, 159, 212, 265, 318, 530, 636, 795, 1060, 1590, 3180

There is a total of 24 positive divisors.
The sum of these divisors is 9072.
The arithmetic mean is 378.

16 even divisors

2, 4, 6, 10, 12, 20, 30, 60, 106, 212, 318, 530, 636, 1060, 1590, 3180

8 odd divisors

1, 3, 5, 15, 53, 159, 265, 795

How to compute the divisors of 3180?

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 3180 by each of the numbers from 1 to 3180 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)

3180 / 1 = 3180 (the remainder is 0, so 1 is a divisor of 3180)
3180 / 2 = 1590 (the remainder is 0, so 2 is a divisor of 3180)
3180 / 3 = 1060 (the remainder is 0, so 3 is a divisor of 3180)
...
3180 / 3179 = 1.0003145643284 (the remainder is 1, so 3179 is not a divisor of 3180)
3180 / 3180 = 1 (the remainder is 0, so 3180 is a divisor of 3180)

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 3180 (i.e. 56.391488719487). 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 $\frac{N}{d} = D$ )

3180 / 1 = 3180 (the remainder is 0, so 1 and 3180 are divisors of 3180)
3180 / 2 = 1590 (the remainder is 0, so 2 and 1590 are divisors of 3180)
3180 / 3 = 1060 (the remainder is 0, so 3 and 1060 are divisors of 3180)
...
3180 / 55 = 57.818181818182 (the remainder is 45, so 55 is not a divisor of 3180)
3180 / 56 = 56.785714285714 (the remainder is 44, so 56 is not a divisor of 3180)