What are the divisors of 3868?

1, 2, 4, 967, 1934, 3868

There is a total of 6 positive divisors.
The sum of these divisors is 6776.
The arithmetic mean is 1129.3333333333.

4 even divisors

2, 4, 1934, 3868

2 odd divisors

1, 967

How to compute the divisors of 3868?

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 3868 by each of the numbers from 1 to 3868 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)

3868 / 1 = 3868 (the remainder is 0, so 1 is a divisor of 3868)
3868 / 2 = 1934 (the remainder is 0, so 2 is a divisor of 3868)
3868 / 3 = 1289.3333333333 (the remainder is 1, so 3 is not a divisor of 3868)
...
3868 / 3867 = 1.0002585983967 (the remainder is 1, so 3867 is not a divisor of 3868)
3868 / 3868 = 1 (the remainder is 0, so 3868 is a divisor of 3868)

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 3868 (i.e. 62.193247221865). 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 $\frac{N}{d} = D$ )

3868 / 1 = 3868 (the remainder is 0, so 1 and 3868 are divisors of 3868)
3868 / 2 = 1934 (the remainder is 0, so 2 and 1934 are divisors of 3868)
3868 / 3 = 1289.3333333333 (the remainder is 1, so 3 is not a divisor of 3868)
...
3868 / 61 = 63.409836065574 (the remainder is 25, so 61 is not a divisor of 3868)
3868 / 62 = 62.387096774194 (the remainder is 24, so 62 is not a divisor of 3868)