What are the divisors of 3826?

1, 2, 1913, 3826

There is a total of 4 positive divisors.
The sum of these divisors is 5742.
The arithmetic mean is 1435.5.

2 even divisors

2, 3826

2 odd divisors

1, 1913

How to compute the divisors of 3826?

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 3826 by each of the numbers from 1 to 3826 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)

3826 / 1 = 3826 (the remainder is 0, so 1 is a divisor of 3826)
3826 / 2 = 1913 (the remainder is 0, so 2 is a divisor of 3826)
3826 / 3 = 1275.3333333333 (the remainder is 1, so 3 is not a divisor of 3826)
...
3826 / 3825 = 1.0002614379085 (the remainder is 1, so 3825 is not a divisor of 3826)
3826 / 3826 = 1 (the remainder is 0, so 3826 is a divisor of 3826)

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 3826 (i.e. 61.854668376768). 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 $\frac{N}{d} = D$ )

3826 / 1 = 3826 (the remainder is 0, so 1 and 3826 are divisors of 3826)
3826 / 2 = 1913 (the remainder is 0, so 2 and 1913 are divisors of 3826)
3826 / 3 = 1275.3333333333 (the remainder is 1, so 3 is not a divisor of 3826)
...
3826 / 60 = 63.766666666667 (the remainder is 46, so 60 is not a divisor of 3826)
3826 / 61 = 62.72131147541 (the remainder is 44, so 61 is not a divisor of 3826)