What are the divisors of 1784?

1, 2, 4, 8, 223, 446, 892, 1784

There is a total of 8 positive divisors.
The sum of these divisors is 3360.
The arithmetic mean is 420.

6 even divisors

2, 4, 8, 446, 892, 1784

2 odd divisors

1, 223

How to compute the divisors of 1784?

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 1784 by each of the numbers from 1 to 1784 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)

1784 / 1 = 1784 (the remainder is 0, so 1 is a divisor of 1784)
1784 / 2 = 892 (the remainder is 0, so 2 is a divisor of 1784)
1784 / 3 = 594.66666666667 (the remainder is 2, so 3 is not a divisor of 1784)
...
1784 / 1783 = 1.0005608524958 (the remainder is 1, so 1783 is not a divisor of 1784)
1784 / 1784 = 1 (the remainder is 0, so 1784 is a divisor of 1784)

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 1784 (i.e. 42.237424163886). 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 $\frac{N}{d} = D$ )

1784 / 1 = 1784 (the remainder is 0, so 1 and 1784 are divisors of 1784)
1784 / 2 = 892 (the remainder is 0, so 2 and 892 are divisors of 1784)
1784 / 3 = 594.66666666667 (the remainder is 2, so 3 is not a divisor of 1784)
...
1784 / 41 = 43.512195121951 (the remainder is 21, so 41 is not a divisor of 1784)
1784 / 42 = 42.47619047619 (the remainder is 20, so 42 is not a divisor of 1784)