What are the divisors of 3714?

1, 2, 3, 6, 619, 1238, 1857, 3714

There is a total of 8 positive divisors.
The sum of these divisors is 7440.
The arithmetic mean is 930.

4 even divisors

2, 6, 1238, 3714

4 odd divisors

1, 3, 619, 1857

How to compute the divisors of 3714?

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 3714 by each of the numbers from 1 to 3714 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)

3714 / 1 = 3714 (the remainder is 0, so 1 is a divisor of 3714)
3714 / 2 = 1857 (the remainder is 0, so 2 is a divisor of 3714)
3714 / 3 = 1238 (the remainder is 0, so 3 is a divisor of 3714)
...
3714 / 3713 = 1.0002693239968 (the remainder is 1, so 3713 is not a divisor of 3714)
3714 / 3714 = 1 (the remainder is 0, so 3714 is a divisor of 3714)

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 3714 (i.e. 60.94259594077). 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 $\frac{N}{d} = D$ )

3714 / 1 = 3714 (the remainder is 0, so 1 and 3714 are divisors of 3714)
3714 / 2 = 1857 (the remainder is 0, so 2 and 1857 are divisors of 3714)
3714 / 3 = 1238 (the remainder is 0, so 3 and 1238 are divisors of 3714)
...
3714 / 59 = 62.949152542373 (the remainder is 56, so 59 is not a divisor of 3714)
3714 / 60 = 61.9 (the remainder is 54, so 60 is not a divisor of 3714)