What are the divisors of 1792?

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 896, 1792

There is a total of 18 positive divisors.
The sum of these divisors is 4088.
The arithmetic mean is 227.11111111111.

16 even divisors

2, 4, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 896, 1792

2 odd divisors

1, 7

How to compute the divisors of 1792?

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 1792 by each of the numbers from 1 to 1792 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)

1792 / 1 = 1792 (the remainder is 0, so 1 is a divisor of 1792)
1792 / 2 = 896 (the remainder is 0, so 2 is a divisor of 1792)
1792 / 3 = 597.33333333333 (the remainder is 1, so 3 is not a divisor of 1792)
...
1792 / 1791 = 1.000558347292 (the remainder is 1, so 1791 is not a divisor of 1792)
1792 / 1792 = 1 (the remainder is 0, so 1792 is a divisor of 1792)

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 1792 (i.e. 42.332020977033). 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 $\frac{N}{d} = D$ )

1792 / 1 = 1792 (the remainder is 0, so 1 and 1792 are divisors of 1792)
1792 / 2 = 896 (the remainder is 0, so 2 and 896 are divisors of 1792)
1792 / 3 = 597.33333333333 (the remainder is 1, so 3 is not a divisor of 1792)
...
1792 / 41 = 43.707317073171 (the remainder is 29, so 41 is not a divisor of 1792)
1792 / 42 = 42.666666666667 (the remainder is 28, so 42 is not a divisor of 1792)