What are the divisors of 3768?

1, 2, 3, 4, 6, 8, 12, 24, 157, 314, 471, 628, 942, 1256, 1884, 3768

There is a total of 16 positive divisors.
The sum of these divisors is 9480.
The arithmetic mean is 592.5.

12 even divisors

2, 4, 6, 8, 12, 24, 314, 628, 942, 1256, 1884, 3768

4 odd divisors

1, 3, 157, 471

How to compute the divisors of 3768?

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 3768 by each of the numbers from 1 to 3768 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)

3768 / 1 = 3768 (the remainder is 0, so 1 is a divisor of 3768)
3768 / 2 = 1884 (the remainder is 0, so 2 is a divisor of 3768)
3768 / 3 = 1256 (the remainder is 0, so 3 is a divisor of 3768)
...
3768 / 3767 = 1.0002654632333 (the remainder is 1, so 3767 is not a divisor of 3768)
3768 / 3768 = 1 (the remainder is 0, so 3768 is a divisor of 3768)

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 3768 (i.e. 61.384037012891). 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 $\frac{N}{d} = D$ )

3768 / 1 = 3768 (the remainder is 0, so 1 and 3768 are divisors of 3768)
3768 / 2 = 1884 (the remainder is 0, so 2 and 1884 are divisors of 3768)
3768 / 3 = 1256 (the remainder is 0, so 3 and 1256 are divisors of 3768)
...
3768 / 60 = 62.8 (the remainder is 48, so 60 is not a divisor of 3768)
3768 / 61 = 61.770491803279 (the remainder is 47, so 61 is not a divisor of 3768)