What are the divisors of 4110?

1, 2, 3, 5, 6, 10, 15, 30, 137, 274, 411, 685, 822, 1370, 2055, 4110

There is a total of 16 positive divisors.
The sum of these divisors is 9936.
The arithmetic mean is 621.

8 even divisors

2, 6, 10, 30, 274, 822, 1370, 4110

8 odd divisors

1, 3, 5, 15, 137, 411, 685, 2055

How to compute the divisors of 4110?

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 4110 by each of the numbers from 1 to 4110 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)

4110 / 1 = 4110 (the remainder is 0, so 1 is a divisor of 4110)
4110 / 2 = 2055 (the remainder is 0, so 2 is a divisor of 4110)
4110 / 3 = 1370 (the remainder is 0, so 3 is a divisor of 4110)
...
4110 / 4109 = 1.0002433682161 (the remainder is 1, so 4109 is not a divisor of 4110)
4110 / 4110 = 1 (the remainder is 0, so 4110 is a divisor of 4110)

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 4110 (i.e. 64.109281699298). 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 $\frac{N}{d} = D$ )

4110 / 1 = 4110 (the remainder is 0, so 1 and 4110 are divisors of 4110)
4110 / 2 = 2055 (the remainder is 0, so 2 and 2055 are divisors of 4110)
4110 / 3 = 1370 (the remainder is 0, so 3 and 1370 are divisors of 4110)
...
4110 / 63 = 65.238095238095 (the remainder is 15, so 63 is not a divisor of 4110)
4110 / 64 = 64.21875 (the remainder is 14, so 64 is not a divisor of 4110)