What are the divisors of 1668?

1, 2, 3, 4, 6, 12, 139, 278, 417, 556, 834, 1668

There is a total of 12 positive divisors.
The sum of these divisors is 3920.
The arithmetic mean is 326.66666666667.

8 even divisors

2, 4, 6, 12, 278, 556, 834, 1668

4 odd divisors

1, 3, 139, 417

How to compute the divisors of 1668?

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 1668 by each of the numbers from 1 to 1668 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)

1668 / 1 = 1668 (the remainder is 0, so 1 is a divisor of 1668)
1668 / 2 = 834 (the remainder is 0, so 2 is a divisor of 1668)
1668 / 3 = 556 (the remainder is 0, so 3 is a divisor of 1668)
...
1668 / 1667 = 1.000599880024 (the remainder is 1, so 1667 is not a divisor of 1668)
1668 / 1668 = 1 (the remainder is 0, so 1668 is a divisor of 1668)

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 1668 (i.e. 40.841155713324). 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 $\frac{N}{d} = D$ )

1668 / 1 = 1668 (the remainder is 0, so 1 and 1668 are divisors of 1668)
1668 / 2 = 834 (the remainder is 0, so 2 and 834 are divisors of 1668)
1668 / 3 = 556 (the remainder is 0, so 3 and 556 are divisors of 1668)
...
1668 / 39 = 42.769230769231 (the remainder is 30, so 39 is not a divisor of 1668)
1668 / 40 = 41.7 (the remainder is 28, so 40 is not a divisor of 1668)