What are the divisors of 3788?

1, 2, 4, 947, 1894, 3788

There is a total of 6 positive divisors.
The sum of these divisors is 6636.
The arithmetic mean is 1106.

4 even divisors

2, 4, 1894, 3788

2 odd divisors

1, 947

How to compute the divisors of 3788?

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 3788 by each of the numbers from 1 to 3788 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)

3788 / 1 = 3788 (the remainder is 0, so 1 is a divisor of 3788)
3788 / 2 = 1894 (the remainder is 0, so 2 is a divisor of 3788)
3788 / 3 = 1262.6666666667 (the remainder is 2, so 3 is not a divisor of 3788)
...
3788 / 3787 = 1.0002640612622 (the remainder is 1, so 3787 is not a divisor of 3788)
3788 / 3788 = 1 (the remainder is 0, so 3788 is a divisor of 3788)

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 3788 (i.e. 61.546730213716). 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 $\frac{N}{d} = D$ )

3788 / 1 = 3788 (the remainder is 0, so 1 and 3788 are divisors of 3788)
3788 / 2 = 1894 (the remainder is 0, so 2 and 1894 are divisors of 3788)
3788 / 3 = 1262.6666666667 (the remainder is 2, so 3 is not a divisor of 3788)
...
3788 / 60 = 63.133333333333 (the remainder is 8, so 60 is not a divisor of 3788)
3788 / 61 = 62.098360655738 (the remainder is 6, so 61 is not a divisor of 3788)