What are the divisors of 3810?

1, 2, 3, 5, 6, 10, 15, 30, 127, 254, 381, 635, 762, 1270, 1905, 3810

There is a total of 16 positive divisors.
The sum of these divisors is 9216.
The arithmetic mean is 576.

8 even divisors

2, 6, 10, 30, 254, 762, 1270, 3810

8 odd divisors

1, 3, 5, 15, 127, 381, 635, 1905

How to compute the divisors of 3810?

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 3810 by each of the numbers from 1 to 3810 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)

3810 / 1 = 3810 (the remainder is 0, so 1 is a divisor of 3810)
3810 / 2 = 1905 (the remainder is 0, so 2 is a divisor of 3810)
3810 / 3 = 1270 (the remainder is 0, so 3 is a divisor of 3810)
...
3810 / 3809 = 1.0002625360987 (the remainder is 1, so 3809 is not a divisor of 3810)
3810 / 3810 = 1 (the remainder is 0, so 3810 is a divisor of 3810)

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 3810 (i.e. 61.725197448044). 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 $\frac{N}{d} = D$ )

3810 / 1 = 3810 (the remainder is 0, so 1 and 3810 are divisors of 3810)
3810 / 2 = 1905 (the remainder is 0, so 2 and 1905 are divisors of 3810)
3810 / 3 = 1270 (the remainder is 0, so 3 and 1270 are divisors of 3810)
...
3810 / 60 = 63.5 (the remainder is 30, so 60 is not a divisor of 3810)
3810 / 61 = 62.459016393443 (the remainder is 28, so 61 is not a divisor of 3810)