What are the divisors of 3914?

1, 2, 19, 38, 103, 206, 1957, 3914

There is a total of 8 positive divisors.
The sum of these divisors is 6240.
The arithmetic mean is 780.

4 even divisors

2, 38, 206, 3914

4 odd divisors

1, 19, 103, 1957

How to compute the divisors of 3914?

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 3914 by each of the numbers from 1 to 3914 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)

3914 / 1 = 3914 (the remainder is 0, so 1 is a divisor of 3914)
3914 / 2 = 1957 (the remainder is 0, so 2 is a divisor of 3914)
3914 / 3 = 1304.6666666667 (the remainder is 2, so 3 is not a divisor of 3914)
...
3914 / 3913 = 1.0002555583951 (the remainder is 1, so 3913 is not a divisor of 3914)
3914 / 3914 = 1 (the remainder is 0, so 3914 is a divisor of 3914)

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 3914 (i.e. 62.561969278468). 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 $\frac{N}{d} = D$ )

3914 / 1 = 3914 (the remainder is 0, so 1 and 3914 are divisors of 3914)
3914 / 2 = 1957 (the remainder is 0, so 2 and 1957 are divisors of 3914)
3914 / 3 = 1304.6666666667 (the remainder is 2, so 3 is not a divisor of 3914)
...
3914 / 61 = 64.16393442623 (the remainder is 10, so 61 is not a divisor of 3914)
3914 / 62 = 63.129032258065 (the remainder is 8, so 62 is not a divisor of 3914)