What are the divisors of 2246?

1, 2, 1123, 2246

There is a total of 4 positive divisors.
The sum of these divisors is 3372.
The arithmetic mean is 843.

2 even divisors

2, 2246

2 odd divisors

1, 1123

How to compute the divisors of 2246?

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 2246 by each of the numbers from 1 to 2246 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)

2246 / 1 = 2246 (the remainder is 0, so 1 is a divisor of 2246)
2246 / 2 = 1123 (the remainder is 0, so 2 is a divisor of 2246)
2246 / 3 = 748.66666666667 (the remainder is 2, so 3 is not a divisor of 2246)
...
2246 / 2245 = 1.0004454342984 (the remainder is 1, so 2245 is not a divisor of 2246)
2246 / 2246 = 1 (the remainder is 0, so 2246 is a divisor of 2246)

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 2246 (i.e. 47.391982444291). 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 $\frac{N}{d} = D$ )

2246 / 1 = 2246 (the remainder is 0, so 1 and 2246 are divisors of 2246)
2246 / 2 = 1123 (the remainder is 0, so 2 and 1123 are divisors of 2246)
2246 / 3 = 748.66666666667 (the remainder is 2, so 3 is not a divisor of 2246)
...
2246 / 46 = 48.826086956522 (the remainder is 38, so 46 is not a divisor of 2246)
2246 / 47 = 47.787234042553 (the remainder is 37, so 47 is not a divisor of 2246)