What are the divisors of 3814?

1, 2, 1907, 3814

There is a total of 4 positive divisors.
The sum of these divisors is 5724.
The arithmetic mean is 1431.

2 even divisors

2, 3814

2 odd divisors

1, 1907

How to compute the divisors of 3814?

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 3814 by each of the numbers from 1 to 3814 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)

3814 / 1 = 3814 (the remainder is 0, so 1 is a divisor of 3814)
3814 / 2 = 1907 (the remainder is 0, so 2 is a divisor of 3814)
3814 / 3 = 1271.3333333333 (the remainder is 1, so 3 is not a divisor of 3814)
...
3814 / 3813 = 1.0002622606871 (the remainder is 1, so 3813 is not a divisor of 3814)
3814 / 3814 = 1 (the remainder is 0, so 3814 is a divisor of 3814)

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 3814 (i.e. 61.757590626578). 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 $\frac{N}{d} = D$ )

3814 / 1 = 3814 (the remainder is 0, so 1 and 3814 are divisors of 3814)
3814 / 2 = 1907 (the remainder is 0, so 2 and 1907 are divisors of 3814)
3814 / 3 = 1271.3333333333 (the remainder is 1, so 3 is not a divisor of 3814)
...
3814 / 60 = 63.566666666667 (the remainder is 34, so 60 is not a divisor of 3814)
3814 / 61 = 62.524590163934 (the remainder is 32, so 61 is not a divisor of 3814)