What are the divisors of 2444?

1, 2, 4, 13, 26, 47, 52, 94, 188, 611, 1222, 2444

There is a total of 12 positive divisors.
The sum of these divisors is 4704.
The arithmetic mean is 392.

8 even divisors

2, 4, 26, 52, 94, 188, 1222, 2444

4 odd divisors

1, 13, 47, 611

How to compute the divisors of 2444?

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 2444 by each of the numbers from 1 to 2444 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)

2444 / 1 = 2444 (the remainder is 0, so 1 is a divisor of 2444)
2444 / 2 = 1222 (the remainder is 0, so 2 is a divisor of 2444)
2444 / 3 = 814.66666666667 (the remainder is 2, so 3 is not a divisor of 2444)
...
2444 / 2443 = 1.0004093327876 (the remainder is 1, so 2443 is not a divisor of 2444)
2444 / 2444 = 1 (the remainder is 0, so 2444 is a divisor of 2444)

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 2444 (i.e. 49.436828377233). 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 $\frac{N}{d} = D$ )

2444 / 1 = 2444 (the remainder is 0, so 1 and 2444 are divisors of 2444)
2444 / 2 = 1222 (the remainder is 0, so 2 and 1222 are divisors of 2444)
2444 / 3 = 814.66666666667 (the remainder is 2, so 3 is not a divisor of 2444)
...
2444 / 48 = 50.916666666667 (the remainder is 44, so 48 is not a divisor of 2444)
2444 / 49 = 49.877551020408 (the remainder is 43, so 49 is not a divisor of 2444)