What are the divisors of 3774?

1, 2, 3, 6, 17, 34, 37, 51, 74, 102, 111, 222, 629, 1258, 1887, 3774

There is a total of 16 positive divisors.
The sum of these divisors is 8208.
The arithmetic mean is 513.

8 even divisors

2, 6, 34, 74, 102, 222, 1258, 3774

8 odd divisors

1, 3, 17, 37, 51, 111, 629, 1887

How to compute the divisors of 3774?

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 3774 by each of the numbers from 1 to 3774 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)

3774 / 1 = 3774 (the remainder is 0, so 1 is a divisor of 3774)
3774 / 2 = 1887 (the remainder is 0, so 2 is a divisor of 3774)
3774 / 3 = 1258 (the remainder is 0, so 3 is a divisor of 3774)
...
3774 / 3773 = 1.0002650410814 (the remainder is 1, so 3773 is not a divisor of 3774)
3774 / 3774 = 1 (the remainder is 0, so 3774 is a divisor of 3774)

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 3774 (i.e. 61.432890213631). 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 $\frac{N}{d} = D$ )

3774 / 1 = 3774 (the remainder is 0, so 1 and 3774 are divisors of 3774)
3774 / 2 = 1887 (the remainder is 0, so 2 and 1887 are divisors of 3774)
3774 / 3 = 1258 (the remainder is 0, so 3 and 1258 are divisors of 3774)
...
3774 / 60 = 62.9 (the remainder is 54, so 60 is not a divisor of 3774)
3774 / 61 = 61.868852459016 (the remainder is 53, so 61 is not a divisor of 3774)