What are the divisors of 3818?

1, 2, 23, 46, 83, 166, 1909, 3818

There is a total of 8 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 756.

4 even divisors

2, 46, 166, 3818

4 odd divisors

1, 23, 83, 1909

How to compute the divisors of 3818?

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 3818 by each of the numbers from 1 to 3818 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)

3818 / 1 = 3818 (the remainder is 0, so 1 is a divisor of 3818)
3818 / 2 = 1909 (the remainder is 0, so 2 is a divisor of 3818)
3818 / 3 = 1272.6666666667 (the remainder is 2, so 3 is not a divisor of 3818)
...
3818 / 3817 = 1.0002619858528 (the remainder is 1, so 3817 is not a divisor of 3818)
3818 / 3818 = 1 (the remainder is 0, so 3818 is a divisor of 3818)

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 3818 (i.e. 61.789966823102). 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 $\frac{N}{d} = D$ )

3818 / 1 = 3818 (the remainder is 0, so 1 and 3818 are divisors of 3818)
3818 / 2 = 1909 (the remainder is 0, so 2 and 1909 are divisors of 3818)
3818 / 3 = 1272.6666666667 (the remainder is 2, so 3 is not a divisor of 3818)
...
3818 / 60 = 63.633333333333 (the remainder is 38, so 60 is not a divisor of 3818)
3818 / 61 = 62.590163934426 (the remainder is 36, so 61 is not a divisor of 3818)