What are the divisors of 3812?

1, 2, 4, 953, 1906, 3812

There is a total of 6 positive divisors.
The sum of these divisors is 6678.
The arithmetic mean is 1113.

4 even divisors

2, 4, 1906, 3812

2 odd divisors

1, 953

How to compute the divisors of 3812?

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 3812 by each of the numbers from 1 to 3812 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)

3812 / 1 = 3812 (the remainder is 0, so 1 is a divisor of 3812)
3812 / 2 = 1906 (the remainder is 0, so 2 is a divisor of 3812)
3812 / 3 = 1270.6666666667 (the remainder is 2, so 3 is not a divisor of 3812)
...
3812 / 3811 = 1.0002623983207 (the remainder is 1, so 3811 is not a divisor of 3812)
3812 / 3812 = 1 (the remainder is 0, so 3812 is a divisor of 3812)

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 3812 (i.e. 61.741396161733). 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 $\frac{N}{d} = D$ )

3812 / 1 = 3812 (the remainder is 0, so 1 and 3812 are divisors of 3812)
3812 / 2 = 1906 (the remainder is 0, so 2 and 1906 are divisors of 3812)
3812 / 3 = 1270.6666666667 (the remainder is 2, so 3 is not a divisor of 3812)
...
3812 / 60 = 63.533333333333 (the remainder is 32, so 60 is not a divisor of 3812)
3812 / 61 = 62.491803278689 (the remainder is 30, so 61 is not a divisor of 3812)