What are the divisors of 1796?

1, 2, 4, 449, 898, 1796

There is a total of 6 positive divisors.
The sum of these divisors is 3150.
The arithmetic mean is 525.

4 even divisors

2, 4, 898, 1796

2 odd divisors

1, 449

How to compute the divisors of 1796?

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 1796 by each of the numbers from 1 to 1796 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)

1796 / 1 = 1796 (the remainder is 0, so 1 is a divisor of 1796)
1796 / 2 = 898 (the remainder is 0, so 2 is a divisor of 1796)
1796 / 3 = 598.66666666667 (the remainder is 2, so 3 is not a divisor of 1796)
...
1796 / 1795 = 1.0005571030641 (the remainder is 1, so 1795 is not a divisor of 1796)
1796 / 1796 = 1 (the remainder is 0, so 1796 is a divisor of 1796)

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 1796 (i.e. 42.379240200834). 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 $\frac{N}{d} = D$ )

1796 / 1 = 1796 (the remainder is 0, so 1 and 1796 are divisors of 1796)
1796 / 2 = 898 (the remainder is 0, so 2 and 898 are divisors of 1796)
1796 / 3 = 598.66666666667 (the remainder is 2, so 3 is not a divisor of 1796)
...
1796 / 41 = 43.80487804878 (the remainder is 33, so 41 is not a divisor of 1796)
1796 / 42 = 42.761904761905 (the remainder is 32, so 42 is not a divisor of 1796)