What are the divisors of 3146?

1, 2, 11, 13, 22, 26, 121, 143, 242, 286, 1573, 3146

There is a total of 12 positive divisors.
The sum of these divisors is 5586.
The arithmetic mean is 465.5.

6 even divisors

2, 22, 26, 242, 286, 3146

6 odd divisors

1, 11, 13, 121, 143, 1573

How to compute the divisors of 3146?

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 3146 by each of the numbers from 1 to 3146 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)

3146 / 1 = 3146 (the remainder is 0, so 1 is a divisor of 3146)
3146 / 2 = 1573 (the remainder is 0, so 2 is a divisor of 3146)
3146 / 3 = 1048.6666666667 (the remainder is 2, so 3 is not a divisor of 3146)
...
3146 / 3145 = 1.0003179650238 (the remainder is 1, so 3145 is not a divisor of 3146)
3146 / 3146 = 1 (the remainder is 0, so 3146 is a divisor of 3146)

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 3146 (i.e. 56.089214649521). 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 $\frac{N}{d} = D$ )

3146 / 1 = 3146 (the remainder is 0, so 1 and 3146 are divisors of 3146)
3146 / 2 = 1573 (the remainder is 0, so 2 and 1573 are divisors of 3146)
3146 / 3 = 1048.6666666667 (the remainder is 2, so 3 is not a divisor of 3146)
...
3146 / 55 = 57.2 (the remainder is 11, so 55 is not a divisor of 3146)
3146 / 56 = 56.178571428571 (the remainder is 10, so 56 is not a divisor of 3146)