What are the divisors of 2046?

1, 2, 3, 6, 11, 22, 31, 33, 62, 66, 93, 186, 341, 682, 1023, 2046

There is a total of 16 positive divisors.
The sum of these divisors is 4608.
The arithmetic mean is 288.

8 even divisors

2, 6, 22, 62, 66, 186, 682, 2046

8 odd divisors

1, 3, 11, 31, 33, 93, 341, 1023

How to compute the divisors of 2046?

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 2046 by each of the numbers from 1 to 2046 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)

2046 / 1 = 2046 (the remainder is 0, so 1 is a divisor of 2046)
2046 / 2 = 1023 (the remainder is 0, so 2 is a divisor of 2046)
2046 / 3 = 682 (the remainder is 0, so 3 is a divisor of 2046)
...
2046 / 2045 = 1.000488997555 (the remainder is 1, so 2045 is not a divisor of 2046)
2046 / 2046 = 1 (the remainder is 0, so 2046 is a divisor of 2046)

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 2046 (i.e. 45.232731511595). 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 $\frac{N}{d} = D$ )

2046 / 1 = 2046 (the remainder is 0, so 1 and 2046 are divisors of 2046)
2046 / 2 = 1023 (the remainder is 0, so 2 and 1023 are divisors of 2046)
2046 / 3 = 682 (the remainder is 0, so 3 and 682 are divisors of 2046)
...
2046 / 44 = 46.5 (the remainder is 22, so 44 is not a divisor of 2046)
2046 / 45 = 45.466666666667 (the remainder is 21, so 45 is not a divisor of 2046)