What are the divisors of 3836?

1, 2, 4, 7, 14, 28, 137, 274, 548, 959, 1918, 3836

There is a total of 12 positive divisors.
The sum of these divisors is 7728.
The arithmetic mean is 644.

8 even divisors

2, 4, 14, 28, 274, 548, 1918, 3836

4 odd divisors

1, 7, 137, 959

How to compute the divisors of 3836?

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 3836 by each of the numbers from 1 to 3836 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)

3836 / 1 = 3836 (the remainder is 0, so 1 is a divisor of 3836)
3836 / 2 = 1918 (the remainder is 0, so 2 is a divisor of 3836)
3836 / 3 = 1278.6666666667 (the remainder is 2, so 3 is not a divisor of 3836)
...
3836 / 3835 = 1.000260756193 (the remainder is 1, so 3835 is not a divisor of 3836)
3836 / 3836 = 1 (the remainder is 0, so 3836 is a divisor of 3836)

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 3836 (i.e. 61.935450268808). 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 $\frac{N}{d} = D$ )

3836 / 1 = 3836 (the remainder is 0, so 1 and 3836 are divisors of 3836)
3836 / 2 = 1918 (the remainder is 0, so 2 and 1918 are divisors of 3836)
3836 / 3 = 1278.6666666667 (the remainder is 2, so 3 is not a divisor of 3836)
...
3836 / 60 = 63.933333333333 (the remainder is 56, so 60 is not a divisor of 3836)
3836 / 61 = 62.885245901639 (the remainder is 54, so 61 is not a divisor of 3836)