What are the divisors of 3784?

1, 2, 4, 8, 11, 22, 43, 44, 86, 88, 172, 344, 473, 946, 1892, 3784

There is a total of 16 positive divisors.
The sum of these divisors is 7920.
The arithmetic mean is 495.

12 even divisors

2, 4, 8, 22, 44, 86, 88, 172, 344, 946, 1892, 3784

4 odd divisors

1, 11, 43, 473

How to compute the divisors of 3784?

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 3784 by each of the numbers from 1 to 3784 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)

3784 / 1 = 3784 (the remainder is 0, so 1 is a divisor of 3784)
3784 / 2 = 1892 (the remainder is 0, so 2 is a divisor of 3784)
3784 / 3 = 1261.3333333333 (the remainder is 1, so 3 is not a divisor of 3784)
...
3784 / 3783 = 1.0002643404705 (the remainder is 1, so 3783 is not a divisor of 3784)
3784 / 3784 = 1 (the remainder is 0, so 3784 is a divisor of 3784)

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 3784 (i.e. 61.514225996919). 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 $\frac{N}{d} = D$ )

3784 / 1 = 3784 (the remainder is 0, so 1 and 3784 are divisors of 3784)
3784 / 2 = 1892 (the remainder is 0, so 2 and 1892 are divisors of 3784)
3784 / 3 = 1261.3333333333 (the remainder is 1, so 3 is not a divisor of 3784)
...
3784 / 60 = 63.066666666667 (the remainder is 4, so 60 is not a divisor of 3784)
3784 / 61 = 62.032786885246 (the remainder is 2, so 61 is not a divisor of 3784)