What are the divisors of 3668?

1, 2, 4, 7, 14, 28, 131, 262, 524, 917, 1834, 3668

There is a total of 12 positive divisors.
The sum of these divisors is 7392.
The arithmetic mean is 616.

8 even divisors

2, 4, 14, 28, 262, 524, 1834, 3668

4 odd divisors

1, 7, 131, 917

How to compute the divisors of 3668?

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 3668 by each of the numbers from 1 to 3668 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)

3668 / 1 = 3668 (the remainder is 0, so 1 is a divisor of 3668)
3668 / 2 = 1834 (the remainder is 0, so 2 is a divisor of 3668)
3668 / 3 = 1222.6666666667 (the remainder is 2, so 3 is not a divisor of 3668)
...
3668 / 3667 = 1.0002727024816 (the remainder is 1, so 3667 is not a divisor of 3668)
3668 / 3668 = 1 (the remainder is 0, so 3668 is a divisor of 3668)

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 3668 (i.e. 60.564015718907). 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 $\frac{N}{d} = D$ )

3668 / 1 = 3668 (the remainder is 0, so 1 and 3668 are divisors of 3668)
3668 / 2 = 1834 (the remainder is 0, so 2 and 1834 are divisors of 3668)
3668 / 3 = 1222.6666666667 (the remainder is 2, so 3 is not a divisor of 3668)
...
3668 / 59 = 62.169491525424 (the remainder is 10, so 59 is not a divisor of 3668)
3668 / 60 = 61.133333333333 (the remainder is 8, so 60 is not a divisor of 3668)