What are the divisors of 1444?

1, 2, 4, 19, 38, 76, 361, 722, 1444

There is a total of 9 positive divisors.
The sum of these divisors is 2667.
The arithmetic mean is 296.33333333333.

6 even divisors

2, 4, 38, 76, 722, 1444

3 odd divisors

1, 19, 361

How to compute the divisors of 1444?

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 1444 by each of the numbers from 1 to 1444 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)

1444 / 1 = 1444 (the remainder is 0, so 1 is a divisor of 1444)
1444 / 2 = 722 (the remainder is 0, so 2 is a divisor of 1444)
1444 / 3 = 481.33333333333 (the remainder is 1, so 3 is not a divisor of 1444)
...
1444 / 1443 = 1.000693000693 (the remainder is 1, so 1443 is not a divisor of 1444)
1444 / 1444 = 1 (the remainder is 0, so 1444 is a divisor of 1444)

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 1444 (i.e. 38). 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 $\frac{N}{d} = D$ )

1444 / 1 = 1444 (the remainder is 0, so 1 and 1444 are divisors of 1444)
1444 / 2 = 722 (the remainder is 0, so 2 and 722 are divisors of 1444)
1444 / 3 = 481.33333333333 (the remainder is 1, so 3 is not a divisor of 1444)
...
1444 / 37 = 39.027027027027 (the remainder is 1, so 37 is not a divisor of 1444)
1444 / 38 = 38 (the remainder is 0, so 38 and 38 are divisors of 1444)